Malbranque was the difference between the two sides as Fulham took revenge for Rovers' 2-0 win at Craven Cottage earlier in the season.
It looked plain sailing for Blackburn when Lucas Neill put them ahead after six minutes with his first goal of the season.
Neill combined with fellow Australian Brett Emerton in a lovely move before shooting home from 12 yards.
Malbranque, a thorn in Blackburn's side throughout, fired Fulham level in the 20th minute from a Brian McBride cross.
Rovers responded to dominate the later stages of the first half with Jonathan Stead, Ryan Nelsen and Morten Gamst Pedersen all missing chances that looked easier to score.
But it was the Cottagers who started the second period on top and they were unlucky to see a goal harshly cancelled out for foul when Zat Knight headed home a corner from Mark Pembridge.
Eight minutes after the restart Fulham's persistence was rewarded when another Pembridge corner found McBride unmarked at the far post and the big American striker's finish was clinical.
Blackburn should have been level in the 56th minute when Emerton burst clear only to see his shot bounce clear off a post, and an even better chance arrived soon after.
Luis Boa Morte was adjudged to have pushed Pedersen in the box but Savage's penalty was saved by Edwin van der Sar.
Then came a crazy two-minute spell during which both teams were reduced to ten men.
First to go was Blackburn skipper Craig Short who pushed over Boa Morte after the Fulham winger had been guilty of a poor challenge on Nelsen.
Fulham's Liam Rosenior followed soon after when he too raised his hands to push over Savage in a moment of madness.
The game developed into something of a farce late on with both teams going in search of further goals, but it was Fulham who found a route through the efforts of Malbranque.
A three-man move resulted in the ball falling for the midfield star, who made no mistake from 12 yards.
Blackburn manager Mark Hughes said: "We found we had no gas left in our tank and it was a poor performance by recent standards.
"Fulham have some tricky players who we never managed to get a grip of and we also contrived to miss several great chances ourselves."
Of Short's dismissal, he added: "Craig is very disappointed but he knows that he can't raise his hands in that fashion."
Fulham manager Chris Coleman said: "Liam has no excuse for what he did but I was pleased with the effort of the team and this is a very timely win after our recent difficulties.
"We showed great character and a lot of composure on the ball too, and it paid dividends.
"We could have fallen to pieces after we went behind but we didn't - the opposite in fact."
Man of the match Steed Malbranque
An outstanding performance from the French playmaker left Blackburn's engine-room facing a nervous breakdown.