EXETER (20) 30
- Tries: Whitehead, Thomas, Dollman
- Cons: Steenson 3
- Pens : Steenson 3
WASPS (20) 23
- Tries: Daly, Varndell
- Cons: L. Thomas 2
- Pens: L. Thomas 2, Bell
Exeter moved up to fifth in the Premiership table by beating Wasps and securing their fifth win of the season.
Elliot Daly and Tom Varndell went over for the visitors, with Chris Whitehead and Haydn Thomas scoring tries for Exeter for a 20-20 half-time scoreline.
Phil Dollman's well-worked try proved decisive for Exeter after the break and Gareth Steenson took his tally with the boot to 15 points.
Tommy Bell's penalty with the game's last kick secured Wasps' bonus point.
Exeter stretched their unbeaten home run to five matches this season while Wasps, who remain eighth in the table, are still searching for their first victory away from home since October 2011.
Steenson's first penalty of the night gave Exeter a third-minute lead, before Lee Thomas made it 3-3 only three minutes later.
A 45-metre effort from Steenson put the Chiefs ahead again, but it was the visitors who scored the game's first try.
Daly led the charge down the middle and evaded Steenson's tackle to go over, with Thomas kicking the extras and then adding a penalty to give Wasps a seven-point advantage.
Joe Simpson was sin-binned for a professional foul and Exeter took full advantage with Whitehead driving over the line, while Steenson successfully landed the conversion.
Wasps stormed back and scored their second try, but it came amid some controversy with Varndell going over after a forward pass from Christian Wade, while Thomas added his second conversion.
The hosts drew level when Haydn Thomas burst through under the posts and Steenson's conversion brought the game level at the break.
Steenson hit the upright with the first penalty after the break, before Wasps were reduced to 14 men as Daly was sent to the sin bin.
Exeter edged in front with Steenson's third successful penalty and then pulled further in front following a great piece of play by Luke Arscott.
His perfectly-weighted kick was caught by Dollman who went over in the corner, while Steenson was accurate with the conversion again.
Replacement Bell cut the deficit to seven with the last kick of the game to secure Wasps a bonus point and move them to within a point of seventh-placed Bath.
VIEWS FROM THE DRESSING ROOM
Exeter head coach Rob Baxter:
"When you get the three tries and you have a little bit of breathing space you are always a little disappointed not to get that fourth try.
"Obviously with five minutes to go and 10 points up there is an opportunity - as you are unlikely to lose the game so you can give it a real crack.
"Unfortunately, how we went about it probably wasn't quite accurate enough.
"But to get three tries and be relatively comfortable for that last third of the game, considering how it was to and fro in the first half, I was really pleased."
Wasps head coach Dai Young:
"I thought we were lucky to come away with a losing bonus point.
"Certainly in the first half we were in the game but in the second half we never had any control, never had any ball, which didn't allow us to put any pressure on.
"For most of the second half we were scrambling and defending our line. Obviously the big decisive factor was our two yellow cards, no complaints from me they were yellow cards, but we had 17 points scored when we were down to 14men. "
Arscott; Nowell, Dollman, Shoemark, Jess; Steenson, Thomas; Sturgess, Whitehead, Rimmer; Hayes (capt), Hanks; Mumm, Scaysbrook, Baxter.
Naqelevuki for Dollman (70), Barrett for Thomas (75), Moon for Sturgess (66), Alcott for Whitehead (67), Tui for Rimmer (64), Muldowney for Hanks (64), Johnson for Scaysbrook (64). Not Used: Mieres.
Southwell (capt); Varndell, Daly, L. Thomas, Wade; Robinson, Simpson; Taulfao, Rhys T. Thomas, Sawinston; Palmer, Wentzel; Johnson, Poff, Vunipola.
T. Bell for L. Thomas (70), Masi for Robinson (64), McIntyre for Taulafo (61), Lindsay for T. Thomas (64), Taylor for Swainston (71), S. Jones for Poff (60). Not Used: Cannon, Davies.
Simpson (27), Daly (51).