George Ford kicked a match-winning conversion with the game's final kick in front of watching England head coach Eddie Jones as Bath dramatically ended Wasps' unbeaten European Champions Cup record with a 25-23 victory.
England ace Ford brilliantly landed the touchline extras to full-back Anthony Watson's try in the third minute of stoppage time after Wasps were reduced to 13 men when French referee Jerome Garces yellow-carded flanker George Smith and substitute prop Lorenzo Cittadini for technical offences.
It followed earlier touchdowns at the Ricoh Arena by centre Jonathan Joseph and wing Matt Banahan, in addition to two Ford penalties and a conversion, as Bath made it two wins from two in Pool Five.
Wasps appeared to have done enough, preserving a 100 per cent group record following comprehensive victories over Leinster and Toulon last month.
Full-back Rob Miller's try midway through the second half put Wasps ahead, while f ly-half Ruaridh Jackson kicked four penalties, centre Elliot Daly landed a long-range strike and Jackson's replacement Jimmy Gopperth struck a late penalty - but it was not to be.
The game started at a breakneck pace, with Bath wing Semesa Rokoduguni breaching Wasps' defence after just two minutes, only to be called back after French referee Jerome Garces spotted a knock-on by England's once-capped wing.
And Wasps then stormed upfield, utilising the blistering pace of Rokodoguni's opposite number Charles Piutau, before some last-gasp Bath defence prevented a try.
It was a frantic contest in the early stages, with both sides continuing to tear into each other after Jackson had kicked Wasps ahead.
Ford tied things up through an angled penalty, and then Bath claimed the game's opening try after a Wasps move broke down near halfway, enabling Joseph to sprint clear from 40 metres out before Ford added the conversion to secure a 10-3 advantage.
Although Daly landed one of his trademark penalties from the halfway line that kept Wasps in touch, Bath added a second try after 23 minutes when Watson fielded a high kick near the touchline, found scrum-half Niko Matawalu in support, and he skipped past opposite number Joe Simpson's challenge to send Banahan over.
Ford could not land the conversion, but Bath were off and running, punishing Wasps' inaccuracy with ball in hand, with Watson and Joseph proving particular threats.
Wasps readily used number eight Nathan Hughes as their midfield focal point of attack, and on a number of occasions he ran purposefully into Bath territory, testing the visitors' front-line defence.
And with Wasps finishing strongly before half-time, Bath conceded two penalties inside their 22 and Jackson made no mistake each time, cutting the deficit to three points at the interval.
Watson required treatment after suffering a knock early in the second period, and the game initially failed to recapture its first-half intensity.
But a long-range Ford penalty restored a six-point advantage for Bath, before the visitors looked to counter-attack from inside their own 22. Rokoduguni spilled possession, though, and Piutau almost capitalised on his blunder, yet he was hauled down just two metres from the line.
Another Jackson penalty brought Wasps back to three points behind, and Bath found themselves under a period of sustained pressure, with their defence finally breached on 58 minutes.
Wasps, displaying far more composure with ball in hand than they had done during the first-half, patiently went through the phases, biding their time before enough space appeared and Miller finished impressively wide out.
Jackson sent the touchline conversion attempt narrowly wide, but there was a clear urgency and defined accuracy about Wasps' game, meaning Bath needed to establish some kind of territorial foothold or face the prospect of defeat.
They could not find a way back into the game, though, and Gopperth's late penalty looked to have done enough for Wasps - but then came the late drama.