Abendanon put in a superb display at the Rec
Bath: (10) 51
Tries: Abendanon 3, Cheeseman, Maddock, Berne, Bory
Cons: Barkley 2, Malone, Berne
Bristol: (12) 12
Tries: Robinson, Lemi
Bath kept their season alive as they reached the European Challenge Cup semi-finals with a second-half demolition of local rivals Bristol.
Nick Abendanon's glorious finish put Bath ahead, but Bristol hit back as Lee Robinson scored and then set up David Lemi to put his side in a 12-10 lead.
Bristol paid the price for a string of penalty misses, as Bath's impressive backs cut loose after the break.
Abendanon completed his hat-trick, as Bath ran in seven second-half tries.
Languishing in eighth place in the Guinness Premiership table, Bath went into the match knowing their season was effectively over if they lost.
Bristol dominated the opening 40 minutes but - after Danny Gray's first penalty miss of the match - they fell behind to a superb try from Abendanon.
Steve Borthwick stole possession at a Bristol line-out, and a classic handling move by the Bath backs gave Abendanon space and the highly-rated full-back showed great skill to beat two defenders.
Robinson caused Bath a lot of problems before the break
The visitors hit back with a try from Robinson after good passing in midfield, and soon after the big winger cut a great line off Gray to set up Lemi for Bristol's second try.
Bath's Olly Barkley hit the post with another penalty attempt but Gray - who otherwise put in a decent display - gave a shocking performance of goal-kicking, missing four kicks before the break.
Barkley redeemed himself with a long-range effort just before the break to send Bath into the break with a spring in their steps at just 12-10 down.
Gray started the second half with yet another awful miss with the boot, and that gave a fired-up Bath just the fillip they needed.
Soon after, Joe Maddock crossed in the corner after Shaun Berne drew the last man to put Bath ahead.
And that score opened the floodgates, with Bristol having no answer to Bath's cutting edge out wide or to the home team's hard-working pack.
Tom Cheeseman just got the ball down on 53 minutes despite a great tackle from Robinson as Bath created an overlap on the left.
There was nobody at home for Bristol in defence five minutes later as Berne burst down an unguarded blind side to score Bath's fourth, and the centre only had to wait two minutes for his second score.
Barkley went into a huge gap in the midfield and drew the full-back to give Berne a stroll to the line.
Next in the queue was Abendanon for his second as Maddock made the most of a two-on-one opportunity, and the outstanding full-back completed his hat-trick after another link-up with the winger.
With the clock ticking down, a delighted home crowd urged Bath to one last attack and, after a fine Andy Williams break, substitute David Bory scored with the conversion bringing up the half century.
Bath head coach Steve Meehan:
"What's important is this squad now recognises it can achieve things.
"Heineken Cup entry through this competition would be fantastic but actually lifting the trophy would be a great reward for the players.
"It was a very good second half and some aspects of play were brilliant but you can't forget the first half when we made some errors that put us under pressure.
"This is a skilful team that is getting better."
Bristol Director of Rugby Richard Hill:
"I'm not sure what happened in the second half - Bath just played exceptionally well.
"This hasn't been a very nice experience - I've got to slink home now in disguise because I still live in Bath. We got a stuffing."
Bath: Nick Abendanon; Joe Maddock, Shaun Berne, Olly Barkley, Tom Cheeseman; Chris Malone, Nick Walshe; David Barnes, Pieter Dixon, Matt Stevens, Steve Borthwick (capt), Danny Grewcock, Andy Beattie, Michael Lipman, Isaac Feaunati.
Replacements: Lee Mears, Aaron Jarvis, Peter Short, Jonny Faamatuainu, Andy Williams, David Bory, Chev Walker.
Bristol: Josh Taumalolo; Lee Robinson, Neil Brew, Sam Cox, David Lemi; Danny Gray, Shaun Perry; Dave Hilton, Mark Regan, Darren Crompton, Mariano Sambucetti, Gareth Llewellyn (capt), Roy Winters, Joe El Abd, Andrew Blowers.
Replacements:David Blaney, Alex Clarke, Nathan Budgett, Craig Short, Greg Nicholls, Jason Strange, Luke Arscott.