After dominating the opening 45 minutes, Paul Ince's side took a deserved lead when Chris Samba headed home Morten Gamst Pedersen's corner on the stroke of half-time.
But Sunderland came roaring back after the break, with Kenwyne Jones netting his second goal in four days after a mistake by Paul Robinson, before Djibril
Cisse lifted the ball over the England keeper 20 minutes from time.
That's now seven league games without a win for Rovers and a much-needed three points for an under-fire Roy Keane.
Blackburn made by far the better start and could have taken the lead with less than two minutes on the clock. Andre Ooijer's ball into the box was headed down by Keith Andrews into the path of Stephen Warnock, who drilled a left-foot shot just past the post.
Rovers continued to dominate the early exchanges, aided by a string of set-pieces.
On seven minutes, a corner routine off the training ground, saw Zurab Khizanishvili connect with Pedersen's corner, but a combination of keeper Marton Fulop and Steed Malbranque scrambled the ball behind.
From the resulting delivery, Roque Santa Cruz leapt brilliantly, but his powerful header came crashing back off the bar.
Pedersen then stung the gloves of Fulop with a fierce free-kick minutes later.
At the other end, Dean Whitehead's long clearance found Jones, whose snap-shot was comfortable for Robinson, whilst Cisse lifted the ball well wide from a similar angle, as he attempted to chip the England international.
However, that was as good as it got for the visitors in the first half, as Andrews' free-kick forced a fine save from Fulop, before Rovers eventually broke
the deadlock from another set-piece.
In the second and final minute of time added on, Pedersen fired over a corner from the left and the towering Samba sent a looping header over Fulop and beyond the reach of the defender on the line.
A goal on the stroke of half-time can be demoralising to some teams, but Sunderland made a superb start to the second-half.
Jones rattled the crossbar from Malbranque's centre just two minutes in and the same duo combined as the visitors equalised just two minutes later. From Malbranque's corner, Robinson's attempted punch was poor and Jones hooked the ball into the top corner from close range.
Kieran Richardson's free-kick forced Robinson to tip over, before Sunderland scored again.
Malbranque was again the provider, heading through to Cisse, who spun past Khizanishvili before cleverly chipping the ball over the onrushing Robinson.
Santa Cruz hit the side-netting and Aaron Mokoena's thunderous strike was deflected wide as Rovers threw everyone forward in the closing stages, but the visitors held out to end a run of four straight defeats.