Bath (10) 15 Tries: Claassens, Skirving Cons: Davis Pens: Davis Wasps (10) 17 Tries: Varndell 2, Lemi Con: Cipriani
Wasps fly-half Danny Cipriani tackles giant Bath wing Matt Banahan
Wasps' Tom Varndell scored his second double in two games before Bath missed a match-levelling conversion with the last kick of the game.
The Premiership match was level at 10-10 after 30 minutes with Varndell's brace cancelling out Michael Claassens' try and five points from Ryan Davis.
David Lemi's converted try then gave Wasps a 17-10 lead at the break.
Bath finally scored in the last minute through Ben Skirving but Davis missed the conversion as Wasps went top.
Wasps followed up their victory over Harlequins at Twickenham on the opening weekend of the season by hanging on with 14 men after their England prop Tim Payne was sent off having received two yellow cards for separate scrum offences in the closing stages.
Referee Chris White played almost 20 minutes of second-half injury time, but although Bath number eight Skirving finally managed to go over for the hosts, Wasps escaped with the points.
The win came despite fly-half Danny Cipriani having an off day with the boot and missing four kicks at goal from five attempts.
Wasps scrum-half Joe Simpson was the star of the show, playing havoc with the Bath defence and helping to create both of Varndell's touchdowns, the second after he made a 60m break.
Bath boss Steve Meehan: "We only played well for 30 minutes. It is a question of application. We know we can play, we have got the talent here, but we have got to sustain it for 80 minutes.
"It was a much better performance than last week, but it still wasn't good enough."
Meehan on Bath not being awarded a late penalty try: "I will look forward to hearing the explanation of why we didn't get one. The fact that Wasps scored three tries was a very disappointing aspect of our game. We just have to be a bit smarter."
Wasps boss Tony Hanks: "We are ecstatic. Not many visiting teams will win down here. We have achieved what we wanted to."
Hanks on Simpson: "Joe's talents are fairly obvious. He is maturing nicely.
"Some of his kicking game was really good today, and he is nailing the core roles of a scrum-half. He has still got a long way to go, but he is developing nicely."
Bath: Maddock; Carraro, Cheeseman, Hape, Banahan; Davis, Claassens; Flatman, Mears, Bell, Hooper, Grewcock, Beattie, Salvi, Skirving. Replacements: Cuthbert for Cheeseman (63), Barnes for Flatman (68), Dixon for Mears (56), Jarvis for Bell (68), Short for Grewcock (56), Faamatuainu for Beattie (56). Not Used: Bemand, Little.
Wasps: Van Gisbergen; Varndell, Jacobs, Kefu, Lemi; Cipriani, Simpson; Payne, Webber, Broster, Skivington, Birkett, Worsley, Betsen, Ward-Smith. Replacements: Walder for van Gisbergen (41), Baker for Broster (72), Hart for Worsley (72), Mitchell for Walder (74). Not Used:Ward, Beech, Leo, Fury.
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