The first half was dominated by Cipriani and the Sale forwards. The one-time England international set up Nick Macleod and Johnny Leota's tries in the opening period, as well as adding a conversion.
Irish's response before the break came through a penalty from Ian Humphreys.
Humphreys kicked two more three-pointers in the second period to reduce the deficit, but two late Cipriani penalties sealed the victory.
Sale went into the game on the back of yet another difficult week which saw the removal of Bryan Redpath as director of rugby.
Redpath was then installed as head coach on Wednesday with chief executive Steve Diamond putting himself in charge of first-team duties.
And that indecisiveness off the field translated to the team early on in this encounter. Straight from the kick-off Cillian Willis was charged down which allowed the visitors to build an attack in the opposition 22.
Topsy Ojo used his searing pace to scythe through the hosts' defence, but he failed to spot the overlap and the move eventually broke down.
Despite their edgy opening, solid set-piece work allowed the Sharks to gain a foothold in the match. After they had stolen an Irish lineout, Sale drove impressively and forced the Reading-based outfit to infringe.
Macleod kicked the resultant opportunity as the home team led 3-0 with eight minutes gone.
It seemed to settle them down and they added to that lead soon after when fly-half Cipriani sent the full-back over.
If anything, it was London Irish who looked like the side who had gone on a horrendous run of defeats with the back three struggling to deal with the wet conditions.
They did reduce the arrears when Humphreys kicked three points, but it was the Sharks who continued to threaten when Leota charged through the defensive line.
Although that did not come to fruition, it was not long before the Samoan outside centre was crossing the try-line.
Once again instigated by Cipriani, the stand-off's wonderfully delayed pass sent Leota through a gap and he shrugged off two would-be tacklers before touching down.
The hosts' fly-half converted to extend their advantage to a deserved 15-3 scoreline at half-time.
But with a team that was so low on confidence, it was never a comfortable lead, especially when Humphreys ate into it just after the interval with a second three-pointer.
Even though the second period became mainly scrappy, it was the visitors who began to create opportunities.
After Humphreys had broken the gain-line, Sale conceded a penalty which the fly-half duly converted.
Irish pressed but the hosts remained composed and Cipriani sealed the victory with successive penalties from the tee.