The Sharks have been rooted to the foot of the table since the start of the campaign but they dug deep to claim a precious victory in a fraught encounter at a windswept Salford City Stadium.
Fly-half Cipriani was steadily influential throughout and claimed a 18-point haul after being dropped for his side's defeat at London Wasps in their previous outing.
He kicked four penalties and converted tries from Richie Gray, James Gaskell and England winger Mark Cueto, whose touchdown saw him draw level with former Sale team-mate Steve Hanley's all-time Premiership try-scoring record of 75.
Worcester opened the scoring in the fifth minute when former England international Andy Goode converted his first penalty.
He added two more in quick succession to increase the visitors' lead to 9-0 after 13 minutes before Sale finally responded in the 21st minute.
Goode took his points tally to 17 in the second half as Neil Best and Matt Kvesic crossed over for the Warriors, who collected a deserved losing bonus point.