Exeter (5) 21
Tries: Johnson, Budgen
Conversions: Steenson Penalties: Mieres 2, Steenson
Wasps (6) 11
Penalties: Davis 2
Exeter fly-half Ignacio Mieres is tackled by Chris Bell during the Chiefs' victory over Wasps
Exeter produced a fine second-half performance to climb to third in the Premiership with victory over Wasps.
Wasps led 6-5 at the break as fly-half Ryan Davis kicked two penalties either side of Tom Johnson's try for Exeter.
Fly-half Ignacio Mieres slotted two penalties and replacement Gareth Steenson another to give the Chiefs breathing space.
A converted Chris Budgen try then sealed victory for the hosts before Jack Wallace scored a late consolation.
Victory took Exeter level on points with second-placed Saracens in the table, with the Chiefs only behind the reigning Premiership champions on points difference.
Davis, a former Chiefs player, kicked Wasps into an early lead following Christian Wade's exciting run, before Exeter were hampered by injuries to wing Nic Sestaret and lock Peter Short.
It was the hard work that we did in the first half, against that strong wind, that laid the foundations
Exeter head coach Rob Baxter
With Wasps reduced to 14 men after Richard Birkett was sent to the sin-bin, the Chiefs hit the front when Johnson capitalised on Sireli Naqelevuki's half break to go over.
But their lead was short-lived as Davis slotted over a second penalty to ensure Wasps went in at half-time with a slender advantage.
Exeter took charge after the break though, with Argentine half-back Mieres kicking them in front with a penalty from two metres inside his own half.
He soon added another before being replaced by Steenson, who himself made no mistake with the boot to put Exeter 14-6 up.
Budgen burrowed his way over for the game's decisive score 17 minutes from time, Steenson adding the conversion, but Wallace burst through the home defence in the closing moments to complete the scoring.
VIEWS FROM THE DRESSING ROOM
Exeter head coach Rob Baxter:
"It was the hard work that we did in the first half, against that strong wind, that laid the foundations.
"We knew that we had to grind away a little and we did that by restricting them to just six points.
"It was getting a decent try on the board that really paid dividends for us in the second half."
Wasps' director of rugby Dai Young:
"Although there are areas of the second half that we can be disappointed with but there were three or four clear opportunities in the first half which we didn't take.
"That was one of the main reasons why we lost and in the second half we didn't keep the ball long enough - because playing in to the wind you have to be very good at keeping hold of the ball.
"Exeter did that well in the first half and it produced opportunities they didn't take - and in the second half I thought Exeter played the conditions better."
Exeter: Arscott, Sestaret, Naqelevuki, Shoemark, Jess, Mieres, Thomas, Sturgess, Whitehead, Tui, Hayes, Short, Johnson, Scaysbrook, Baxter.
Replacements: Rennie for Sestaret (7), Steenson for Mieres (55), Barrett for Thomas (67), Moon for Sturgess (73), Clark for Whitehead (54), Budgen for Tui (47), Muldowney for Short (23), White for Johnson (68).
Wasps: Haughton, Varndell, Bell, Flutey, Wade, Davis, Berry, Payne, Webber, Baker, Birkett, Wentzel, Launchbury, Poff, Filipo.
Replacements: Wallace for Haughton (66), Daly for Bell (73), Holmes for Berry (66), Castex for Payne (45), Lindsay for Webber (72), McIntyre for Baker (63), Burton for Wentzel (67), Everard for Launchbury (78).
Sin-Bin: Birkett (26).
Ref: Martin Fox (RFU).