Netani Talei is tackled by Wasps' George Skivington and Dan Ward-Smith
Wasps maintained their play-off bid and plunged bottom club Worcester deeper into relegation trouble at Sixways.
The visitors raced into a 21-3 lead with two tries from centre Dominic Waldouck and one from flanker Tom Rees.
Captain Pat Sanderson touched down and Willie Walker kicked eight points to keep Worcester in touch at half-time.
But Danny Cipriani, who kicked nine points in all, landed a penalty to make it 24-13 as a late converted Alex Grove try earned Warriors a bonus point.
The result leaves Worcester two points adrift of nearest rivals Leeds, who they travel to next Sunday, with just two games remaining.
And defeat at Headingley could end their six-year stint in the Premiership.
Wasps, whose England prop Phil Vickery came off the bench following a six-month absence with a neck injury, leapfrogged London Irish, who host Leeds on Sunday, to go fourth.
Worcester coach Mike Ruddock: "Leeds are a well-organised team and they will be very difficult on their own patch but we have to deliver, it is as simple as that.
"If there was a league table for passion, desire and commitment, we would be top of it after our performance today. We went toe to toe with one of the best teams in Europe.
"We went 21-3 behind, and a lot of sides would have dropped their heads, but we dominated the game after that.
"I wanted the win today, and we weren't a million miles away after a bad start. There were so many positives, but unfortunately it is another loss and the league table doesn't lie."
Wasps director of rugby Tony Hanks: "I thought Dominic Waldouck was outstanding. We lost our shape in attack and defence when he went off.
"He's got a real good feel for the game and is playing with a lot of confidence. I think he is due a chance [with England].
"You don't come to Worcester expecting a bonus point, but it is disappointing because we started well enough to give ourselves the chance of one.
"We've kept ourselves in the hunt in terms of the play-offs, and we have a huge fixture next weekend against a team [Bath] that is playing very well."
Replacements: Grove for Rasmussen (28), Jones for Tuitupou (68), Powell for Arr (71), C. Black for A. Black (41), Fortey for Lutui (61), Sourgens for Taumoepeau (57), Gillies for Rawlinson (64), Cracknell for Sanderson (55).
Replacements: van Gisbergen for Waldouck (27), Walder for Cipriani (69), Payne for Taulafo (60), Vickery for Broster (54), Worsley for Shaw (53), Betsen for Hart (61).
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