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.
The result lifted Sale to within one point of second-bottom London Irish and encouraged hopes that survival is within their grasp.
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.
With the wind at their backs, 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.
They won their first line-out and forced Worcester back towards their own line before towering forward Gray touched down under a pack of bodies.
Cipriani converted to cut Worcester's lead to just two points and the pendulum swung firmly in Sale's favour.
Yet Worcester claimed their first try in the 27th minute when Matt Kvesic's simple offload sent fellow flanker Neil Best burrowing over the line from close range.
Goode converted with ease to put Worcester 16-7 ahead but the visitors lost full-back Chris Pennell to the sin-bin 10 minutes before the break for holding down.
Three minutes before half-time, and with Worcester down to 14 men, Sale hauled themselves back into the game with a well-worked try.
They won a line-out on the left flank, switched play to the right corner before Cipriani and hooker Marc Jones combined to send Gaskell over unopposed inside the left channel.
Cipriani converted to leave the scores neatly poised at 16-14 in Worcester's favour at half-time, an advantage extended two minutes after the break when Goode kicked his fourth penalty.
Worcester were reduced to 14 men again in the 45th minute as Walker was then sin-binned for a deliberate knock-on and Cipriani kicked the resultant penalty.
He then landed a penalty from almost 50 metres to put Sale ahead for the first time in the 54th minute before Goode missed from distance moments later.
Sale replacement Fraser McKenzie was then sin-binned within a minute of his introduction for flattening Semisi Taulava and Goode kicked the penalty to edge Worcester back in front.
However, Sale struck a decisive blow in the 59th minute when Gray's astute offload found Richie Vernon and he cleverly sent Cueto scampering over in the left corner.
Cipriani landed a fine conversion to put Sale 27-22 ahead before Goode missed a relatively straightforward penalty.
Cipriani then kicked two more penalties with aplomb before a scrappy late try in the right corner from Kvesic - which Goode failed to convert - gave Worcester a deserved losing bonus point.
- Sports & Recreation