Exeter remain unbeaten at Sandy Park this season as they moved up to fifth place in the Aviva Premiership table, for at least 24 hours.
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The scores were level at 20-20 at half-time, with both sides scoring two tries in the second quarter - the visitors' second coming from a blatant forward pass which questions why TMOs are not at every Premiership match.
Both sides battled and were battered after the break with the Chiefs scoring a converted try and a penalty, while Wasps secured a losing bonus point with a penalty from replacement Tommy Bell just before the final whistle.
Exeter, buoyed by their win at London Irish last Sunday, named an unchanged starting line-up and replacements bench for this encounter.
The visitors made three changes from the starting line-up that beat Leicester 14-12, with Lee Thomas at inside centre, Samoan international Zak Taulafo at loosehead prop and England's Tom Palmer in the second row.
The Chiefs took the game to the visitors and they were rewarded with a penalty after just three minutes when the opposition failed to roll away from the breakdown and fly-half Gareth Steenson slotted the ball between the uprights.
The home side were guilty of the same offence minutes later at the other end and centre Luke Thomas levelled the scores from just inside the 22.
However, Steenson replied with a 45-metre penalty after the visitors failed to roll away at the tackle.
The first tryscoring opportunity came the way of Wasps but wing Tom Varndell was unable to cleanly take the pass as full-back Luke Arscott was guarding his own line and the Chiefs cleared upfield at the resultant scrum.
The visitors continued to look dangerous as fly-half Nick Robinson put a grubber kick through but Varndell was unable to collect. But the pressure continued as centre Elliot Daly burst through to squeeze in at the corner.
Thomas added the extras and then added his second penalty from 22 metres as the Chiefs strayed offside as they defended their line.
The home side then mounted an attack from inside their own 22 through Steenson, who raced away with centre Phil Dollman up in support to take on the charge - but was stopped 10 metres short. London Wasps scrum-half Joe Simpson was yellow carded for a professional foul at the tackle.
Exeter took advantage of the extra man and the scrum drove over the line with hooker Chris Whitehead getting the touchdown and Steenson added the extras to again draw the scores level.
The referee and his assistants were then caught napping as Christian Wade put Varndell clear with a clear forward pass but with no TMO the try was awarded, to the disgust of the Sandy Park crowd and Thomas again converted.
Varndell was then forced to take the ball back over his own line as Arscott was chasing a kick ahead from centre Jason Shoemark. At the scrum Haydn Thomas picked up at the base and the scrum half went over under the sticks with Steenson converting.
With the scores level at 20-20 at the break, the Chiefs started the second period strongly but missed a chance to take the lead when Steenson's penalty from out on the right hit the far upright.
Wing Jack Nowell broke and then chipped ahead but was taken out by Daly and referee Andrew Small showed the outside centre a yellow card, Steenson's penalty putting the Chiefs back in front.
The Chiefs looked set to take advantage of the extra man at the pick and drive with prop Brett Sturgess coming the closest to crossing the whitewash - but the home side were penalised for going off their feet.
Still with the extra man the Chiefs kept battering the Wasps line, working the ball into the middle where Arscott perfectly kicked ahead and Dollman collected before diving over in the corner. Steenson converted from the touchline.
Wasps secured a losing bonus point with Bell's penalty at the end - but their search for a first victory on the road in the league since October 2011 continues.