The Chiefs secured a bonus point before the break as Thomas Waldrom scored two tries and Jack Nowell and Mitch Lees also crossed the whitewash.
Frank Halai replied for Wasps on the stroke of half-time and Ashley Johnson and Lorenzo Cittadini scored after the restart to pull the home side level.
Waldrom then completed his hat-trick before Moray Low's late try secured a convincing victory for the visitors.
Exeter put in a clinical display in the first half, scoring four tries in the first 34 minutes for a 27-6 lead, with Jimmy Gopperth kicking two penalties for Wasps in reply.
But George Smith's grubber kick allowed Halai to score in the corner right on the half-time whistle and Gopperth converted to make it 27-13 at the break.
Johnson and Cittadini powered over to drag Wasps level on 52 minutes but Chiefs number eight Waldrom crashed over to seal his hat-trick and put Exeter back ahead.
After losing Henry Slade to a knee injury midway through the second half, Exeter asserted their control and Low bundled over for their sixth try of the afternoon.
The Chiefs will be replaced at the top of the table if unbeaten Saracens beat Newcastle Falcons on Sunday.
Wasps director of rugby Dai Young:
"Today was a real leveller and brought us back down to earth.
"We were beaten by a very good Exeter team that looked to be better than us in all departments. Sometimes you just have to put your hand up and say that.
"We were hugely disappointing in the driving at the line-out and that is something we pride ourselves on. Today Exeter made it look easy.
"You've got to give them credit but in saying that we have to be better than we were today. It tends to happen when people start saying nice things about you and you have to be careful not to believe it."
Exeter director of rugby Rob Baxter:
"The performance was very good. Credit to Wasps, I was surprised how well they fought back into it.
"Wasps have had some big emotional performances in the last few weeks. They are draining and sometimes it's hard to hit the field with that same intensity.
"Our challenge was to try and put a bit of pressure on Wasps with our line speed, put pressure on their scoreboard and see if they had been drained by those two previous games."
Wasps: Piutau; Tagicakibau, Daly, Jacobs, Halai; Gopperth, Simpson; Mullan, Johnson, Cittadini, Davies, Gaskell, Jones, Smith, Thompson.
Replacements: Shervington, McIntyre, Cooper-Wooley, Myall, Hughes, Simpson, Jackson, Leiua.
Exeter: Dollman; Nowell, Slade, Hill, Short; Steenson, Chudley; Moon, Yeandle (capt), Francis, Lees, Parling, Johnson, Salvi, Waldrom.
Replacements: Taione, Rimmer, Low, Welch, White, Lewis, Whitten, Woodburn.
Referee: Greg Garner.
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Exeter went top of the Premiership table after a thrilling win over Wasps.