Two Joe Carlisle penalties were enough for Worcester to move above Wasps and secure their first away win in the Premiership since April 2009.
Carlisle gave Warriors the lead with a penalty on the stroke of half-time.
And he doubled the visitors' lead in a scrappy match at Adams Park with another kick in the second half.
The victory means Warriors have moved above Wasps into 10th place with Bath now in ninth following their victory at home against London Irish.
Wasps are on their worst run in the Premiership for 10 years having now lost five matches in a row.
Worcester lost debutant Samoan number eight Ezra Taylor after just two minutes and five seconds as he was carried off the field on a stretcher with a serious knee injury that was later revealed to be a ruptured patella.
Wasps director of rugby Dai Young:
"We're in a dogfight with four or five other teams, scrapping for our lives but we're not in any better or worse position than any of them.
"There is no point panicking. Chucking all the bricks out of the pram doesn't get you anywhere.
"We played all the rugby and Worcester never threatened us. "But the handling was disappointing with ball in hand, our ball retention was not good enough and we never turned pressure into points.
"We've got to keep working. We know we can do it, we've had some good results in Europe. We're not a million miles from it."
Worcester head coach Richard Hill:
"It's a big one for us; it means we can start to look upwards rather than over our shoulder at Newcastle.
"I know Wasps were understrength but they have the most potent three-quarter line in the Premiership so when we saw the rain coming down we were pleased.
"We edged the kicking battle and the territory. Wasps did attack from deep but this wasn't the weather for it."
Wasps: Haughton; Varndell, Waldouck, Flutey, Wade; Robinson, Simpson; Payne, Webber, Broster; Birkett, Wentzel (capt); Du Plessis, Poff, Jones.
Replacements: Mayor for Wade (31), Davis for N. Robinson (34), Berry for Simpson (70), O'Donoghue for Birkett (67), Everard for Jones (74).Not Used: Lindsay, Baker, Castex.
Worcester: Pennell (capt); Garvey, Grove, Rasmussen, Benjamin; Carlisle, Arr; Mullan, Lutui, Tomaszczyk; Percival, Jones; Betty, Kvesic, Taylor.
Replacements: Perry for Arr (40), Shervington for Lutui (57), Taumoepeau for Tomaszczyk (26), Abbott for Taylor (2).Not Used: Douglas, Gulliver, Goode, Fatiaki.
Sin Bin: Garvey (46).
Referee: Wayne Barnes (RFU).