England international Barkley, who joins French club Racing Metro next week, kicked 16 points, including the conversions of prop David Wilson's try and a late penalty try during a mistake-riddled Recreation Ground clash.
Bath skipper Stuart Hooper also scored, and although Sale delivered a second-half Johnny Leota try converted by Nick Macleod, who slotted an early penalty, the Sharks remain in 12th and last place with just one point.
They dispensed with the services of their forwards coach Steve Scott last weekend two days after a home defeat against newly-promoted London Welsh, and Sharks chief executive Steve Diamond has temporarily taken on that role in support of rugby director Bryan Redpath.
But although Sale competed aggressively at the breakdown - and they looked a far more fluent attacking force after Danny Cipriani appeared as a second-half substitute - there was nothing to seriously suggest an immediate upturn in fortunes.
The current campaign already represents their worst start to a Premiership season during its 15-year existence, but life is not about too get any easier, with Leicester awaiting them next Friday night.
Redpath responded to his team's dismal run by making six changes, which included Macleod replacing former England fly-half Cipriani, but they also arrived in the west country without injured internationals Richie Gray and Dwayne Peel.
Barkley led Bath out, and it took him just 12 minutes to make an impression when he kicked two penalties in quick succession after his opposite number Macleod missed an earlier long-range chance.
Sale offered plenty of endeavour and effort, but Bath looked more dangerous in attack, and they dominated territory despite Macleod cutting Sale's deficit to three points.
Barkley, the third highest points scorer in Premiership history behind Charlie Hodgson and Andy Goode, booted Bath 12-3 ahead with two further penalties as Sale struggled to secure meaningful possession.
And the visitors' cause was not helped six minutes before the break when wing Tom Brady received a yellow card following a dangerous challenge on Bath flanker Ben Skirving.
Skirving, tipped over in mid-air by Brady from a restart, was uninjured, but Sale could now only look to end the opening period without suffering further damage on the scoreboard.
Macleod missed a second penalty chance from three attempts as the interval approached, and although Bath trooped off 12-3 ahead they would have gained little satisfaction from a disjointed, error-strewn opening period.
It took them just eight minutes of the second period, though, to score the game's first try, and it was Wilson who injected much-needed ambition.
His initial surge took him inside Sale's 22, and when the visitors ran out of defensive numbers it was Wilson who crashed over from close range, touching the ball down down one-handed.
Barkley added the conversion, but Sale hit back after 59 minutes when concerted and patient work through the phases ended in Leota collecting a try that Macleod converted.
Redpath sent Cipriani on for the final 15 minutes, and his first contribution was a touch-finder that took Sale back into Bath's 22.
There was far more urgency about the visitors than at any other time in the game, and Cipriani's clever chip into space almost produced a try as Bath found themselves under sustained pressure.
Had Sale possessed more attacking composure, then Bath might have been in serious trouble, but they stormed back upfield and their forwards rumbled over, with Hooper the beneficiary.
Hooper's try sealed the win for Bath, yet even at this early stage of the Premiership season, they look ill-equipped to finish higher than mid-table.
And to complete a miserable afternoon for Sale, they ended the game with 14 men when their Wales international number eight Andy Powell was sin-binned for a high tackle and Bath capitalised by claiming a penalty try when Sale pulled down a scrum on their line.
Winger Adam Thompstone scored a hat-trick on his first start as Leicester bounced back from last week's home defeat to Harlequins with a superb 30-8 victory over Exeter at Welford Road.
Thompstone, signed from London Irish in the summer, scored one in the first half and two in the second, with England fly-half Toby Flood kicking 15 points in a fine all-round performance. Replacement Ben White scored a last-minute consolation try for Exeter.
Despite suffering from an injury crisis, Leicester were too strong for an Exeter side who showed none of the form which earned them the double over the Tigers last season and the scalp of Saracens last week.
Leicester's injury problems intensified when three players - hooker George Chuter, full-back Scott Hamilton and prop Boris Stankovich - withdrew on the day of the game, taking the total on the treatment table to 12.
They were also under pressure after last week's home defeat by leaders Harlequins and having gone 166 minutes without scoring a try, their worst barren run since November 2010.
In contrast, Exeter made just two changes, England international Tom Johnson coming into the back row and Kiwi Jason Shoemark into the centre.
Following their success here last term, Exeter were attempting to join a select band of teams - Northampton, Saracens, Harlequins and Wasps - who had managed back-to-back league wins at Welford Road.
And they drew first blood when fly-half Ignacio Mieres banged over a 49-metre penalty after just two minutes.
Leicester, however, hit back in impressive style and dominated the rest of the half with the pack taking control and Flood pulling the strings behind.
It was Flood's inside pass to Vereniki Goneva which gave Leicester the breakthrough, the Fijian winger bursting into the Exeter 22 and Thompstone finishing off the move with a try in the right corner.
Flood kicked the touchline conversion and made in 10-3 six minutes later with a penalty from a similar position.
Mieres missed with a penalty from a metre inside his own half before Johnson, prop Brett Sturgess and centre Sireli Naqelevuki sparked Exeter's best move which only failed to produce a try because of some great scrambling defence by Leicester.
Leicester turned defence into attack after a great scrum on their line and then rejected the chance of another three points by opting for the line out and drive, the move breaking down when Flood failed to find Goneva with a long floated pass.
Flood did, however, end the half on a high note with penalties in the 30th and 40th minutes to stretch Leicester's lead to 16-3.
Exeter started the second half strongly, Naqelevuki bursting into the 22 before ruining his good work with an attempted pass behind his back which went forward.
And Leicester made the visitors pay by working their way up field and scoring their second try through Thompstone, his former Irish team-mate Dan Bowden providing the scoring pass with Flood adding the conversion.
The try was made by the pressure Thomas Waldrom put on the Exeter defence and also the fact that he took out Mieres off the ball, an incident the referee missed and the TMO did not appear to take into account.
With their tails up the Tigers piled on the pressure and giant Samoan prop Logovi'i Mulipola had an easy chance to score but lost the ball in the tackle over the line.
Exeter, however, began to find some form and exerted strong pressure on Leicester without rattling the scoreboard. After a couple of good moves down either wing they went for the catch and drive but Leicester stole their line out ball.
And Leicester stretched their lead to 30-3 with 13 minutes left after a turnover in their own half. Flood countered and Matt Smith chipped through for Thompstone to complete his hat-trick. Flood added the conversion.
With the last attack of the game, replacement White scored for Exeter from close range, the TMO awarding the try after long deliberation, but Gareth Steenson missed the conversion.
- Nick Macleod