The ex-England number 10 scored a try in the dying minutes and kicked three penalties and two conversions as the Sharks collected the points in their pursuit of a top-six place that would give them a lucrative European Champions Cup spot next season.
Full-back Mike Haley and replacement TJ Ioane added further Sale tries, while Irish scored tries from full-back Sean Maitland and centre Johnny Williams, with fly-half Greig Tonks kicking a penalty and conversion.
Sale wanted a big win over the basement side to keep on the tails of sixth-placed Harlequins and got off to a good start when their early pressure brought a penalty from Cipriani..
The Exiles, however, showed enough in the opening quarter of the match to give them some positive hope of survival in their relegation dogfight with Newcastle Falcons.
They have just three matches left to stay up including a potential decider at Newcastle's Kingston Park on April 17.
Tonks levelled matters on 14 minutes with a 26-metre penalty before Irish took the lead with a sparkling touchdown.
Number eight Ofisa Treviranus found a tiny gap in midfield on the Sale 22 and fed scrum-half Scott Steele who, in turn, gave the ball inside for Maitland to scorch over unopposed.
The conversion should have been simple but, somehow, Tonks managed to miss it and, with two other penalty misses in the half, eight points went begging.
Sale had their chances despite the Irish dominance. They could have got at try in the left corner but hooker Tommy Taylor knocked on with the line only five metres away.
However, for all their effort, Irish went into the break behind as those missed kicks from Tonks came back to haunt them.
Sale went over for a well-worked converted try from Haley, and the visitors kept the heat on the Exiles after the break as veteran scrum-half Peter Stringer and Cipriani controlled matters behind their powerful pack.
And, when Irish reached into Sale territory, they had little to counter a solid defence
Eventually, the Sharks extended their lead when Cipriani booted his third penalty of the day from 26 metres .
Just at it seemed Sale would fly away to record a comfortable ninth win of the season, they received a rude reminder that Irish were not going to give up without a fight as the Exiles pulled back to within a point.
Try-machine Williams bustled his way over after being put in on the left by skipper Luke Narraway.
Tonks was made up for past errors and landed a giant touchline conversion. There was just one point in it.
Yet, just as Irish thought they were back, Sale replied with two more late tries, the first from Ioane and then an interception by Cipriani on halfway which saw him run under the posts. The fly-half converted both to finish things off.