Vickery was helped off with suspected concussion
Wasps: 28 (15)
Tries: Lewsey, Reddan, Doherty
Cons: King, Van Gisbergen
Pens: King, Van Gisbergen 2
Bristol: 0 (0)
Wasps hammered second-placed Bristol in their Guinness Premiership encounter on Sunday but lost England captain Phil Vickery in the process.
The prop was forced off with suspected concussion after he appeared to be felled by a punch from Bristol's Jason Hobson after 64 minutes.
Tries from Josh Lewsey and Eoin Reddan helped Wasps lead 15-0 at half-time.
Two Mark van Gisbergen penalties edged them further ahead before David Doherty added a third try for the hosts.
The first half saw numerous handling errors in the wet conditions and Wasps were not helped by fly-half Alex King missing three penalties.
King did manage to land one kick to put the hosts into the lead before Lewsey scored the first try after 31 minutes following a slick handling move.
Reddan added a second try just before the break, converted by King, and Wasps continued to hold the upper hand after the interval.
Van Gisbergen took over the kicking duties and added two penalties before the incident involving Vickery.
Play continued as Vickery received treatment on the pitch and Doherty charged through the Bristol defence for Wasps' third try.
Van Gisbergen added the extras but Wasps could not claim a bonus point for scoring four tries as Bristol just managed to repel a series of late attacks.
Wasps director of rugby Ian McGeechan:
"Phil Vickery took a heavy blow so we got the message on the field to get him off.
"I didn't want to mess around as there had been heavy contact. He's fine now."
Wasps coach Shaun Edwards:
"That's as good a performance as I've been involved in during my five years here.
"I can't remember us putting in a performance like that against a top-four team."
Bristol boss Richard Hill:
"It must have been a big haymaker to put that bull (Vickery) down - I'll have to have a look at that. It's not on if that was the case.
"It was a poor day all round for us against a Wasps side who were fired up. They played very well, very clinically and we gave too many penalties away.
"Thank God it wasn't a sunny day. The heavy conditions saved us from a 40-point hammering."
Wasps: Van Gisbergen; Lewsey, Waters, Waldouck, Voyce; King, Reddan; Payne, Ward, Vickery, Shaw, Palmer, Worsley, Rees, Haskell.
Replacements: Ibanez, Adams, Leo, Dallaglio, Amor, Brooks, Doherty.
Bristol: Taumalolo; Robinson, Brew, Higgitt, Lemi; Strange, Perry; Hilton, Regan, Crompton, Hohneck, Llewellyn, Budgett, El Abd, Lewis.
Replacements: Linkmater, Hobson, Winters, Blowers, O'Riordan, Gray, Morgan.
Referee: Roy Maybank