The Chiefs had to settle for a losing bonus point, after Gareth Steenson had kicked three first-half penalties, as they remain in eighth place - but crucially 12 points outside the top four.
After a two-week break from Premiership action for the RBS 6 Nations, Exeter went into this game in front of a sell-out crowd at Sandy Park on the back of victories over London Welsh and reigning champions Harlequins.
Head coach Rob Baxter had set his side the target of building on their two successes in a bid to continue their play-off aspirations, as well as achieving a second season of Heineken Cup rugby.
The home side were forced to make two late changes with flanker James Scaysbrook, whose wife gave birth earlier in the day, and centre Sireli Naqelevuki missing out due to a knee injury. Jason Shoemark and Dave Ewers came in.
Leicester, who beat the Chiefs 30-8 at Welford Road in September, had England internationals Tom Youngs, Dan Cole, Geoff Parling, Tom Croft, Ben Youngs, Toby Flood and Manu Tuilagi in their starting line-up.
Flood led the Tigers for the first time in the absence of both Geordan Murphy and Louis Deacon while Leicester's director of rugby Richard Cockerill included Martin Castrogiovanni in the squad as front row cover.
The sides were evenly matched in the opening minutes but it was Exeter who got the first points on the board after 10 minutes through a 30-metre penalty from fly-half Steenson.
But after a period of sustained pressure the visitors were back on level terms, just before the midway point of the half, as Flood landed a simple 15-metre penalty after the Chiefs had strayed offside.
The Exeter scrum were outmuscled in the front row and conceded three penalties with Flood slotting the third through the uprights. The home side hit back immediately with Steenson's second after lock Dean Mumm was taken out at the line-out.
Flood's third penalty, from 38 metres in front of the posts, nudged the Tigers back into the lead to set up a crucial final 10 minutes of the half - but neither side had been able to make any real progress when in the opposition 22.
Leicester looked set to score the opening try in the final minutes of the half as Ben Youngs passed outside to Matthew Tait - but, with a three overlap, the full-back took the wrong option and was tackled short of the line by wing Jack Nowell.
Shoemark was able to clear upfield which led, after a Tait knock-on and wing Niall Morris offside, to Steenson landing his third penalty of the half from close to the left touchline and level the scores at 9-9.
Both sides upped the pace at the start of the second half and with 25 minutes remaining both clubs brought on reinforcements as legs began to tire.
The introduction of Castrogiovanni did little to strengthen the Tigers' efforts as the Italy international was troubled by Chiefs Carl Rimmer and was pinged for standing-up.
Then, after a short break from Flood, Castrogiovanni was penalised on the Chiefs 22 for crossing.
Flood took advantage of the wind at his back and landed a 35-metre penalty to put Leicester back in to the lead with 10 minutes remaining.
The home side won a penalty in the final minute when Castrogiovanni was penalised for collapsing the scrum - but Steenson's attempt from the left touchline fell just short of the target.