Cipriani’s brilliant cross kick in the 78th minute was gathered by wing Josh Bassett, who strolled over for Wasps third try and put the game to bed.
On an afternoon of slapstick passing and missed opportunities last year’s beaten finalists were relieved to get out of Sixways in one piece and with four points in the bag.
And director of rugby Dai Young admitted the match was too close for comfort and his side were not firing.
“I always felt we had another gear and we would just do enough to win that game but it was pretty cruel that Worcester didn’t get a bonus point,” he said.
“It was not a great performance from us but we have the win and these are games you can lose. I don’t think any team is playing the way they would like to play and we certainly are not.”
Worcester were hamstrung by the loss of tight-head prop Nick Schonert after 24 seconds, with a suspected broken angle, and struggled in the scrum all afternoon.
Marcus Watson, brother of England’s Anthony, conjured the first score for Wasps with a cunning kick in-field that he gathered to roll over and finished to help his side lead 10-7 at the break.
Worcester had been furious when they had a try chalked off for obstruction by Sam Lewis when Tom Heathcote went over in the 23rd minute.
Willie le Roux finished off a slick move to stretch the lead, before Cipriani finished Worcester off.
Worcester director of rugby Gary Gold said: “I don’t think our character can be questioned but we need more accuracy. Scrums became very difficult with Nick off.”
Worcester – Try: Alo; Con: Heathcote; Pen: Olver.
Wasps – Tries: Watson, Le Roux, Bassett; Cons: Gopperth (3); Pen: Gopperth.