Scrum-half Haydn Thomas gave the visitors the perfect start with a try on five minutes and the Chiefs led throughout from there on.
The Scarlets, who saw Wales fly-half Rhys Priestland carried from the field with an ankle injury in the second half, did grab back a late penalty try from a scrum but it was not enough as they crashed to a third straight European defeat.
The Scarlets were without wing George North with a hip injury but six Wales squad members returned to their starting line-up including Jonathan Davies who captained the region.
Exeter made six changes with Argentina winger Gonzalo Camacho starting and centre Sireli Naqelevuki returning to the side.
The Scarlets went through the phases after Richard Kelly won the kick-off but it was the Chiefs who made their mark with their first-ever Heineken Cup try after five minutes.
From a scrum full-back Luke Arscott made a break through midfield and Thomas was on his shoulder to go over. Steenson added the extras.
But the Scarlets responded almost immediately with a 30-metre penalty from Priestland to make it 7-3 after eight minutes.
That Scarlets score was cancelled out on 12 minutes with a Steenson penalty after the home pack had stood up in a scrum on their line.
Both sides were forced into significant changes in personnel. Scarlets lost tight-head prop Lee and Chiefs replaced Thomas.
And Steenson was on target again to extend the Chiefs lead to 10 points after Scarlets were caught offside from an Aled Davies box kick.
The Scarlets got themselves in a good attacking position but knocked the ball on at a ruck with Andy Fenby isolated.
But from the resulting scrum the Scarlets earned a penalty on the 30-minute mark which Priestland converted.
Chiefs responded with a third Steenson penalty after the Scarlets found themselves under pressure at the scrum, while Priestland missed a penalty from inside his own penalty two minutes before the interval.
The Chiefs produced an impressive attack from the kick off but a knock-on five metres out prevented them extending their 16-6 interval lead.
The Scarlets suffered a real setback when Priestland was carried off after picking up an ankle injury when he slipped when in possession. He was replaced by Aled Thomas.
And it got worse for the home side as Steenson was on target with his fourth penalty goal on 49 minutes to restore a 13-point lead.
Aled Thomas kicked a fine long range penalty but that was cancelled out four minutes later with Steenson's fifth penalty shot as Chiefs led 22-9 on the hour mark.
But despite their lead the Chiefs were forced to defend their 22 and in the process lost prop Ben Moon to the sin bin for collapsing a scrum.
And with the extra man the Scarlets earned a penalty try from French referee Mathieu Raynal on 67 minutes to cut the Chiefs lead to 22-16.
The Scarlets went in search of the winning score but despite hammering at Exeter's 22 the visitors held on for a famous win.
Jonny Wilkinson's Toulon made it three wins out of three in Pool Six but did little to justify their tag of favourites with an unconvincing 17-6 victory against struggling Sale.
Filthy conditions at the Salford City Stadium did much to bridge the gulf in class between a star-studded side leading the French Top 14 and one propping up the Aviva Premiership, but the visitors did just enough to secure the crucial points, with winger David Smith scoring the only try and Wilkinson kicking four penalties from seven attempts.
A second defeat to French opposition ahead of next week's re-match on the Cote D'Azure leaves the Sharks with little hope of qualification for the knockout stages, but their priority is survival in the Premiership and new director of rugby John Mitchell will doubtless be encouraged by the gritty display.
Sale's points came from the boot of Danny Cipriani, who was promoted to the starting line-up following the late withdrawal of Cameron Shepherd through illness and the switch of Rob Miller to full-back.
Miller had a superb game in his regular position while Cipriani held his own against the vastly experienced Wilkinson, but the Sharks were unable to carve out a single clear-cut tryscoring chance.
Cipriani drew first blood in the duel of former England fly-halves, landing a 45-metre penalty after seven minutes to put his side into the lead, five minutes after the Toulon captain had been wide with a 40-metre kick.
Wilkinson levelled the scores with a penalty from in front of the posts on 16 minutes as the game developed into a kicking contest.
With conditions worsening in the constant drizzle, Cipriani attempted to secure further points with the boot but was narrowly off target with two ambitious penalty attempts from the halfway line.
Wilkinson also fluffed a third goal-kick on 29 minutes but the visitors scored the game's first try immediately afterwards after Smith found some rare space out on the Sale right.
Cipriani kept the Sharks well in contention with another penalty seven minutes before the interval but Wilkinson responded with his second successful kick three minutes later to make it 11-6 at half-time.
Sale enjoyed the better of the third quarter but Toulon number eight Chris Masoe broke up a promising move by intercepting Cipriani's pass and his 50-metre break set up the position for Wilkinson to kick his third penalty on 51 minutes to open up an eight-point lead.
That gave Toulon, who included a trio of former Sale favourites in Andrew Sheridan, Juan Martin Fernandez Lobbe and Sebastian Bruno, a useful cushion to become more adventurous.
They almost scored a second try when flanker Steffon Armitage was driven over the line but he was unable to ground the ball, while replacement scrum-half Sebastien Tillous-Borde had a last-minute try disallowed by the television match official.
Wilkinson was wide with a drop-goal attempt but he wrapped up the scoring with a fourth penalty.
Ronan O'Gara's right boot helped Munster to a narrow 15-9 win in a cagey clash with Saracens at Thomond Park.
O'Gara had a five-from-five kicking return, whereas his young counterpart Owen Farrell missed four of his seven shots at the posts.
Farrell redeemed himself by converting a 79th-minute penalty for a losing bonus point which keeps Saracens at the top of Pool 1, albeit with Munster now level on 10 points ahead of next week's return fixture in Watford.
This absorbing encounter was balanced on a knife edge throughout, with Munster gaining the early edge to take a 9-3 interval lead.
The immense physicality spilled over at times, leading to yellow cards for Donncha O'Callaghan and Rhys Gills, while Saracens' lineout creased alarmingly under pressure from the hosts.
With man-of-the-match James Coughlan producing the goods up front, O'Gara hammered over two more kicks to stretch the lead to nine points although Farrell had the final say by coolly completing his penalty hat-trick in the dying minutes.
Saracens welcomed back Alex Goode, Chris Ashton, Brad Barritt and IRB Player of the Year nominee Farrell from international duty.
Amid a back row injury crisis, Munster handed a Heineken Cup debut to Cork youngster David O'Callaghan and a back problem continues to rule out former captain Paul O'Connell.
Munster set the early intensity, Will Fraser being caught offside and O'Gara confidently knocked over the left-sided penalty in the fifth minute for the lead score.
A neatly-worked lineout move put Conor Murray dummying past both Schalk Brits and Charlie Hodgson, however an awkward final pass was spilled by the supporting Simon Zebo.
The first sign of a try-scoring threat from the Englishmen was visible in the 12th minute. Goode countered from deep and linked with Barritt and Ashton with the latter's dinked kick grounded just in time by the retreating Felix Jones.
Farrell failed with his first penalty attempt after Mike Sherry went off his feet at a midfield ruck, and a loose Sarries lineout saw O'Gara drill Munster back downfield.
The first flashpoint, midway through the half, resulted in French referee Pascal Gauzere flashing yellow cards to O'Callaghan and Gill for an off-the-ball dust-up that led to others piling in.
Munster exerted pressure on Saracens' lineout again and turnover ball paved the way for O'Gara's second penalty goal, following good carries from James Coughlan and David O'Callaghan.
The sides swapped penalties coming up to half-time, with Farrell punishing a scrum infringement and O'Gara converting after Ernst Joubert had interfered with Donncha O'Callaghan in a lineout.
O'Gara, who was benched during Ireland's November internationals, drifted a drop goal wide in the last act of a tense and feverish first half.
Saracens made the stronger start to the second period, benefiting from some further indiscipline at the breakdown from Munster. A 37-metre penalty from Farrell increased the heat on Rob Penney's men.
The home forwards produced a storming response, winning a scrum against the head before O'Gara fired over his fourth sure-footed strike from inside the Sarries' 22.
A fifth followed as Munster began to dominate in the possession stakes, with Keith Earls and James Downey probing in the middle and the back row working ferociously as a unit.
Saracens were living off Munster mistakes and Farrell drifted a 44-metre penalty to the left and wide as the drizzle came down.
There was glimpse of Farrell's talent in the build-up with a deft flicked pass to Goode creating the space for Fraser's opportunity. Yet, Munster held out and rebounded for an edgy final 10 minutes.
Howlett and Ashton both threatened on their wings, the latter's touchline dart earning a 75th minute penalty which Farrell sent wide off the left hand upright.
But O'Gara blundered as he pushed the resulting drop-out straight into touch. Sarries steeled themselves for a final charge and the fruits of their labour could yet prove vital when the pool placings are decided next month.
Harlequins remain on course for top spot in Pool Three after a comprehensive 57-14 victory over Zebre in Parma.
The Aviva Premiership pacesetters ran in eight tries to secure a winning bonus point.
Sam Smith scored a brace with Nick Easter, Matt Hopper, Rob Buchanan and Ben Botica also among the scorers for Connor O'Shea's high fliers, who also managed two scrum penalty tries.
The most Zebre could manage on a bitterly cold day was a first-half breakaway try by Leonardo Sarto and a late consolation for Alberto Chillon.
With Biarritz losing to Connacht on Friday, Quins' destiny now lies in their own hands and victory in next week's return against Zebre will effectively seal their passage through to the quarter-finals.
Harlequins were good value for their win and barely had to break sweat for some of their tries.
The first came for Smith on 26 minutes, a routine dash for the corner after the Zebre defence had been stretched on the back of a Maurie Fa'asavalu turnover.
Evans converted, adding to an earlier penalty, and already it looked as though the game was up for a desperately limited Zebre side, who failed to get out of their own half in the opening half hour.
Things went from bad to worse for the hapless Italians when serial offender Mauro Bergamasco was sent to the sin-bin for a ruck offence.
With that it looked as though the floodgates would open, and Smith helped himself to a second try after linking superbly with Tom Williams.
Again Evans converted to leave Quins 17-0 up and coasting.
Complacency cost Quins as they went in search of a third try before half-time, and it was Zebre who instead struck next, Sarto racing away after one too many passes cost Quins.
It was shortlived joy for Zebre, and Quins were back in business within three minutes of the restart as Easter bagged their third try after the visiting forwards wrestled the home pack into submission.
Danny Care, Matt Hopper and Mike Brown all went close to adding a fourth, but in the end it was the forwards that took the plaudits, forcing a penalty try after dominating the home scrum.
They would do so again later in the half as Zebre went into meltdown, and sandwiched in between was a fine individual try by Hopper, who showed great footwork to outmanoeuvre the home defence.
He was eclipsed shortly after, however, by substitute prop Buchanan, who scored with practically his first touch after another irresistible attack by rampant Quins.
A late try by Chillon proved scant consolation for a disillusioned Zebre, and it was left to another substitute, Botica, to wrap up the scoring for Quins.
Toulouse put the Ospreys to the sword with a rampant second-half performance to take control of Pool Two after this 30-14 triumph.
The four-time winners led by just 12 points at the interval thanks to quick-fire tries from Florian Fritz and Yannick Nyanga.
The Ospreys hit back with a try from Kahn Fotuali'i but the second half was a one-team affair as Vincent Clerc, Census Johnson, Yoann Huget all crossed.
The visitors again responded with a try, this time from Ryan Bevington, but it was too little too late.
The victory sees the French giants stretch their lead at the top of the group to eight points with Leicester set to face Benetton Treviso on Sunday.
Luke McAlister fired an early penalty wide but Toulouse quickly established a lead thanks to Fritz.
The French hosts looked to launch an attack from the top of a lineout which broke down, but Fritz pounced on the loose ball and sliced through the Ospreys' defence.
McAlister slotted the conversion and seven minutes later they doubled their advantage.
Again, Toulouse were fortunate to capitalise on disarray at the lineout. Gary Botha overthrew and James King flapped the ball towards the Ospreys but it fell straight to Nyanga, who raced home.
But the Welsh region fought back, with ever-present Kahn Fotuali'i and Ashley Beck leading the charge.
And it was the in-form duo that manufactured the Ospreys' opening score. Beck put his side on the front foot with a strong charge that earned a penalty, Fotuali'i caught Toulouse off guard with a quick tap to race clear.
The Welsh region continued to pile on the pressure but Toulouse weathered the storm to go into the break leading 12-7.
But the French side came out firing following the break and their giant pack steamrolled the Ospreys.
They could have hit back within minutes of the restart as Toulouse flooded forward while chasing a McAlister chip but Fotuali'i intervened.
Toulouse continued to dominate and could have been awarded a penalty try following a succession of scrums, but the Ospreys survived and Justin Tipuric snatched a vital turnover.
But Toulouse were relentless and they came close once again after Medard collected McAlister's cross kick.
They were eventually rewarded for their hard work as Picamoles broke from the back of scrum.
The giant number eight charged towards the Ospreys before releasing Burgess with an offload. Clerc received the ball out wide with plenty of work to do, but he rounded Eli Walker to squeeze in the corner.
McAlister failed to add the conversion but Toulouse did not let up with Picamoles continuing to run riot.
After receiving the ball from Albacete he drew in three defenders before sending Johnson over in the same corner.
Doussain faired no better than McAlister from the touchline but the try had sealed the bonus point and established a commanding 22-7 lead.
And there was still time for a fifth try with Doussain and Medard combining for Huget to dance through the Ospreys defence.
To their credit the Welsh region refused to throw in the towel and they hit back with a score of their own as Bevington and Tipuric combined with a football style one-two for the prop to crash over.
Matthew Morgan converted but the try was merely a consolation and Toulouse rubbed salt into their wounds with a Doussain penalty at the death.
Racing Metro kept their hopes alive with a hard fought 19-9 victory over Edinburgh at Stade Yves du Manoir.
Tries from Juan Jose Imhoff and Eddy Ben Arous either side of the interval proved the difference as the Scottish outfit remained winless in the competition.
Edinburgh stay bottom of Pool One, with no points to their name, but they restored some pride with the committed performance.
Edinburgh had failed to score a single point in 160 minutes of rugby as they fell to humiliating defeats to Saracens and Munster in the opening rounds of the competition.
But it took them just two minutes for them to open their account in Paris as Greig Laidlaw dissected the posts.
A scintillating break from Richie Rees should have led to a first try of the campaign, but the Wales international became isolated and was tackled by Juan Martin Hernandez.
Edinburgh continued to dominate the early exchanges, but were unable to turn pressure into points and Racing hit back through the boot of Olly Barkley on 10 minutes.
Michael Bradley's men continued to waste scoring opportunities as Laidlaw fired two penalties in quick succession wide and the big-spending French club punished their Scottish rivals for their lack of killer instinct with the game's opening try.
Fabrice Metz made the initial inroads and some slick handling released Imhoff, who danced around Tom Brown to score.
Barkley failed to add the extras, but the try handed his side an unlikely 8-3 lead.
Racing were buoyed by their score and came close to grabbing a quick-fire second following a sustained period of pressure, but Edinburgh survived.
But they were still unable to take advantage of point-scoring opportunities as another Laidlaw effort fell short before he made some amends with the final kick of the half.
Edinburgh were once again the better side in the opening exchanges following the restart, but they were unable to turn pressure into points.
They opted for the corner as they looked to force a try, but lost possession and conceded a penalty as Racing escaped unpunished.
And the Parisians were again quick to punish the visitors. They launched wave after wave of attacks and, although Edinburgh initially survived, it was only a matter of time until Racing broke through.
They won the ball from the top of a five-metre lineout and launched a powerful rolling maul that left Edinburgh in disarray before crashing over the try-line with Arous the beneficiary.
Edinburgh responded through the boot of Laidlaw, but they were dealt a blow when Brown was stretchered off after a heavy collision with Juan Pablo Orlandi.
Edinburgh refused to thrown in the towel and continued to battle, but Maxime Machenaud put the result beyond doubt with a penalty with just minutes to spare.