A first-half try from Matt Banahan had put the hosts 10-6 up at the break, and further scores from wings Tom Biggs and Kyle Eastmond, the latter's first since joining the club, sealed the win, with Olly Barkley adding 15 points with the boot.
Two Nicky Robinson penalties had kept Wasps in it and Tom Varndell and Christian Wade crossed in the second half but, as with their surrender of a 27-point lead against Quins last week, it was missed tackles and unforced errors that did for Dai Young's side.
Fly-half Freddie Burns kicked 25 points and created the try which swung the match out of nothing as Gloucester recorded their first win of the season 40-31 against London Irish.
They bounced back from the 24-19 opening-day home defeat by Northampton to come from behind three times.
England number eight Ben Morgan, with his first try for his new club, winger James Simpson-Daniel and replacement flanker Akapusi Qera, touched down for Gloucester with Burns landing seven penalties and two conversions.
Right-wing Topsy Ojo scored the Exiles' opening try with Ireland scrum-half Tomas O'Leary and replacement prop Halani Aulika marking their home debuts with tries.
Fly-half Steven Shingler kicked four penalties and two conversions for a 16-point haul.
England centre Manu Tuilagi produced a fabulous two-try performance as Leicester Tigers chalked up their second successive bonus point win of the season with a 34-26 victory over Worcester Warriors at Welford Road.
They scored five tries altogether, the others coming from Fiji winger Vereniki Goneva, lock Graham Kitchener and a penalty try.
Winger David Lemi and centre Alex Grove scored Worcester's tries with former England fly-half Andy Goode kicking 16 points.
Charlie Hodgson again returned to haunt Sale, whose first game at their new Salford City Stadium home ended in defeat a 23-16 defeat to Saracens.
Hodgson, who joined Sarries just over a year ago, last season kicked his new side to victory with 20 points at Edgeley Park - the Sharks' home for the previous eight campaigns. On Saturday the veteran fly-half, who retired from international rugby over the summer, landed 18 points.
Hodgson and opposite number Danny Cipriani, making his home debut following his move from Melbourne Rebels, kicked all the first-half points from penalties as the visitors led 12-9 at the break. Will Addison's breakaway try at the start of the second period briefly put the Sharks ahead, but Chris Ashton's third try in two games for Sarries and Hodgson's boot earned victory.