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Wasps ended Bristol's 10-match unbeaten home record with a clinical display of finishing in muddy conditions at the Memorial Stadium.
The Londoners moved third behind runaway Premiership leaders and champions-elect Leicester and second-placed Northampton through tries from full-back Josh Lewsey, flanker Joe Worsley and lock Joe Beardshaw.
It means that if Tigers beat Welford Road visitors Newcastle next Saturday, and Wasps lose at Bath, then Leicester will take the league title for a remarkable third successive season.
But should Wasps win, then Martin Johnson and company must wait a little longer before cracking open the champagne.
Delaying the inevitable it might be, yet Wasps are now the only team capable of keeping those celebrations on ice.
All their tries came during a 19-minute spell either side of half-time, leaving Bristol to reflect on what might have been after an aggressive forward effort deserved far better.
Bristol's backs were the problem, offering nothing in attack, a display which badly let down the contribution of a juggernaut pack.
Bristol's misery behind the scrum was emphasised on 32 minutes when wild parties thrown out by centre Eduardo Simone and full-back Lee Best enabled Wasps to claim an unlikely 75-metre breakaway score.
Rob Henderson galloped clear, and with Bristol's defence non-existent Lewsey finished things off.
Worsley's was the short-range injury-time effort gave Bristol a second half mountain climb, and four Philipe Contepomi penalties predictably proved insufficient.
Beardshaw's try, a superb effort which rewarded excellent approach work featuring the impressive Kenny Logan and flanker Paul Volley, meant the game was up for Bristol with more than a quarter of the match still remaining.
Wasps went flat out for a bonus point during the closing 20 minutes, but they were denied by a combination of poor handling and spirited Bristol defence.
England hooker Phil Greening made his first Premiership appearance of 2001, going on as a 63rd minute substitute Trevor Leota and showing no ill-effects of knee surgery that has sidelined him since early December.
Bristol, whose last home defeat in any competition was against London Irish last September, kept plugging away, yet despite the promptings of their mercurial skipper Agustin Pichot, there was no invention outside him to make a telling difference.
Logan and Contepomi exchanged early penalties, and the only other talking points of a scrappy first period until Lewsey's try, were separate flare-ups between Leota and his opposite number Neil McCarthy another incident involving Pichot and Wasps wing Paul Sampson.
Once the visitors had established a worthwhile lead though, there was no stopping them as the experience of players like captain Lawrence Dallaglio, prop Will Green and Logan shone through.
The only potential blot on Wasps' landscape was an injury to Irish star Henderson, who was helped from the field on 74 minutes clutching his arm.
BRISTOL : 12
LONDON WASPS : 24
Tries:Josh Lewsey, Joe Worsley, Joe Beardshaw
Cons: Kenny Logan 3