Leicester moved into the Aviva Premiership's top three as they denied battling Exeter in the second half at Sandy Park.
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The home side found themselves with a mountain to climb after tries from scrum-half Ben Youngs and centre Niki Goneva plus a penalty and conversion from fly-half Toby Flood put Leicester 15-0 up at the break.
Home fly-half Gareth Steenson landed three penalties after the break to reduce the arrears to just six points but Flood left the Chiefs without even a losing bonus point for their efforts as he booted two more penalties to seal a 21-9 victory.
The Leicester pack were the key element in the match. They tortured the Chiefs for the whole game in the scrum and secured countless penalties, some at crucial times as Exeter threatened to get a try which would have thrown the game right into the melting pot.
Video official Trevor Fisher was called into action within four minutes of kick-off when Flood chipped over the home defence inside the 22 only for full-back Niall Morris to fluff a certain try with a knock-on over the line.
Leicester should have been even further in front at the break than 15-0 as Flood was guilty of missing a relatively easy penalty from 30 metres and also the conversion of Youngs' well-worked try as hooker Tom Youngs fed him from a rolling maul down the Exeter right.
Flood eventually made up for his errors with a straightforward penalty but that was it until moments before the interval as Exeter eventually came out of reverse gear and found something to threaten the Tigers.
But they could not take the chances they created, one excellent attacking line-out saw Louis Deacon pull out a brilliant catch to steal possession.
The nearest that Exeter got to any score in the first period was a long-range penalty from Steenson which drifted side the right post.
Exeter made things even tougher for themselves with some weak passing when they had some possession and that eventually led to another big blow when centre Jason Shoemark threw a wild pass on halfway which Goneva intercepted and he raced to the line, with Flood booting the conversion.
Exeter had to be more precise if they were to gain anything from the match and Baxter's half-time words seemed to have worked initially when Steenson found his range to boot a penalty and the Chiefs hit back.
They pressed again near the Leicester line and won another penalty directly in front of the posts, a simple three points for Steenson. He added a third on the hour from close range and suddenly Exeter, who lost last season's corresponding clash 12-9, were back in it.
Flood increased the Leicester lead to nine points again with his second penalty but Exeter, with nothing to lose, began running the ball and threatened to score only for their hands to let them down.
That only meant that England prop Dan Cole and the rest of his dominant Tigers front five simply shoved the Chiefs' eight into the ground, which produced penalties that Flood cleared downfield.
And when Exeter illegally went over the top of a ruck with six minutes left, Flood landed another penalty which settled the contest.