Exeter Chiefs Jack Nowell celebrates scoring against Wasps in the Aviva Premiership final
Nathan Hughes, Wasps' massive Fiji-born No8 who became a mainstay in Eddie Jones' England squad in the absence of Billy Vunipola, started to throw his weight around as the Coventry-based side were forced to defend aggressively in the first 10 minutes.
But the Exeter possession eventually told and Jack Nowell wriggled through a defensive gap and crossed over in the corner for the first score of the match.
Wasps were then hit by the withdrawal of Hughes for a Head Injury Assesment and the Chiefs continued to pile on the pressure.
They did not concede in the eight minutes he was off but did so two minutes after his return.
Gareth Steenson's boot sealed a dramatic win for Exeter Chiefs
Ollie Devoto straightened his run off an attack scrum and produced a brilliant, back-door offload to put Phil Dollman in from five metres out.
Gareth Steenson added his second conversion of the match to put the Chiefs firmly in control but Wasps had a sting in their tail in the first half.
Jimmy Gopperth grabbed his 10th try of the 2016/17 season in overtime at the end of the first period, going under the posts to cut the lead to just four at the break.
After half-time, the same pattern resumed with the Chiefs pushing in the Wasps 22.
Wasps and James Haskell were left devastated by the late defeat
But Hughes was once again instrumental, turning the ball over before shrugging off four tacklers in a rampaging run.
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With full-back Dollman down injured, Wasps recycled quickly and Christian Wade's kick in behind bounced kindly for Elliot Daly, who was more than grateful the opportunity to crown a brilliant year with a Premiership final try.
Dollman would not recover and was forced off injured in the same week that he was called up to the Wales squad for the first time at the age of 32.
Head coach Dai Young, interviewed by BT Sport midway through the second half, cited his side's patience as the reason for the fightback as they continued in the ascendancy past the hour mark.
But Exeter were not done yet.
Wasps were on the defensive for much of the game against the Exeter Chiefs
Renewed by a complete replacement of the front row, the 2016 runners-up set up camp on the Wasps tryline, at one point go through 30 phases in search of a go-ahead score.
Wasps held strong though, showing spectacular determination with Gopperth the unlikely hero time and again in breakdown area, eventually getting out of their own half for the first time in what felt like an age with five minutes to go.
Eventually their resistance broke, Hughes penalised for hands in the ruck with less than a minute left to force 20 minutes of extra time.
Both sides looked out on their feet and an injury to Marty Moore force Matt Mullan to return to the Wasps front row.
But the fresh legs had little impact as the frenetic final had taken its toll on the two teams, although Exeter retained the bulk of possession.
With two tries apiece, a place-kicking shootout loomed as neither side could find a score until Chiefs forced a penalty at scrum time on the Wasps five-metre line, Steenson putting the ball over with just 130 seconds to go.
Nowell dived on the restart and the side from the south west saw out the clock to avenge the 2016 defeat.