It was a game of two halves at Ewood Park with Rovers enjoying the better of the opening half, as they laid siege to the Sunderland goal.
Roque Santa Cruz sent a header against the bar while Marton Fulop pulled off a a number of good saves before edging ahead thanks to Christopher Samba, who headed home Morten Gamst Pederson's corner in stoppage time.
However, the Black Cats hit back after the break and were rewarded for their domination with two goals to pick up a first win in five games and avenge Wednesday's Carling Cup defeat to Rovers by the same score line at the Stadium of Light.
The visitors came flying out of the blocks in the second half as Jones thumped a header off the crossbar from Steed Malbranque's cross on 47 minutes, before firing his side level two minutes later. Robinson blocked his header at goal, but the big striker managed to hook the rebound back into the corner of the net from close range.
The Black Cats went in search of a winner and it came on 71 minutes when Malbranque's ball forward found Cisse, who managed to lift it over the advancing Robinson and into the empty net.
Rovers enjoyed their best spell in the last ten minutes as they fought to salvage a point. But apart from Aaron Mokoena's effort from a corner being blocked by Anton Ferdinand near the line, Sunderland held out for the vital win.