Wasps had edged 6-5 in front at the interval, with two penalties from Ryan Davis either side of an Exeter try from Tom Johnson.
But Exeter decisively went ahead when Ignacio Mieres booted two penalties, and Gareth Steenson, who replaced Mieres, kicked one himself before converting a try from Chris Budgen to give the home side a handsome 21-6 lead.
Wasps crossed for their only try of the match with a minute remaining, Jack Wallace touching down, but it came too late to make a real difference.
Exeter coach Rob Baxter made three changes to the team which narrowly lost at Bath last weekend, as Luke Arscott started at full-back, Sireli Naqelevuki was fielded at outside centre and Richard Baxter played at number eight.
Wasps director of rugby Dai Young also made three personnel changes in the wake of a home defeat to Sale, as Bob Baker, Richard Birkett and Riki Flutey came in. Former All Black Ross Filipo switched from the second row to number eight.
Wasps moved ahead after five minutes from a turnover ball inside their own half. Wing Christian Wade broke through and looked to have passed Arscott but the full-back caught him around the ankle.
The Chiefs conceded a penalty and fly-half Ryan Davis, the former Exeter half back, stepped up to landed the three points from 30 metres out, close to the right touchline.
The home side suffered another blow when wing Nic Sestaret was led from the field by the medical staff after he took a heavy knock, to be replaced by centre Bryan Rennie.
Exeter wasted a scoring opportunity from a catch and drive before they gained valuable ground prior to Wasps collapsing the maul.
A kick to the corner saw the lineout lost and the visitors were able clear their line.
Just before the midway point in the half Davis had an opportunity to increase the Wasps lead but the former England Under-21 player saw his 40-metre kick from out on the left float across the face of the posts.
Exeter lock Peter Short was carried off after 23 minutes with an ankle injury and was replaced by Aly Muldowney. Then after another good driving maul from a lineout, Wasps lock Birkett was sent to the sin-bin.
Having turned down three kickable penalty attempts in the half, Naqelevuki made a break before putting blindside flanker Johnson through for the first try of the game.
Argentinian fly-half Mieres, kicking into the wind, hooked his conversion attempt.
Davis, who was off target with his second penalty attempt, found the target from his next opportunity to nudge Wasps back in front.
Exeter went looking to score early in the second half and when the Chiefs were awarded a penalty Mieres made no mistake with a huge kick from two metres inside his own half.
The Chiefs pressed the Wasps line, with scrum-half Haydn Thomas finding a gap opening up in front of him to take the home side up to the 22.
From the next phase they gained a penalty in front of the posts and Mieres stretched the Exeter lead.
Midway through the half Tom Varndell collected close to the Chiefs right corner but was denied when he looked like scoring.
The Chiefs soon won another penalty and replacement fly-half Steenson slotted the ball between the uprights.
Left wing Matt Jess was stopped short of the Wasps line and when the ball was recycled the Chiefs forwards powered over the line and, after consulting television match official Tony Spreadbury, referee Martin Fox awarded the try for Budgen which Steenson converted.
Exeter went in search of another try which would have taken them up to second place in the table above Saracens, who they host next Saturday, on points difference.
But it was Davis who made the break in the opposite direction, before offloading to replacement Wallace who raced down the right to score Wasps' only try of the game.
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