Malbranque also came up with the decider against Wigan Athletic last Monday and this shot on the run from Luis Boa Morte's pass was unerring as it flashed inside David James' near post.
"I am delighted," said the Fulham manager, Chris Coleman. "Especially with the fashion we did it in, although we rode our luck in the second half.
"It was a great finish by Malbranque. He's a quality, quality player and we're absolutely desperate to extend his contract."
Stuart Pearce's City have gone two months without a League home victory and were earlier picked off when Boa Morte sprinted into the area on to Brian McBride's pass and pulled back for the substitute Collins John to fire in off the post.
"We didn't have enough about us to kill the game when we went in front, " Pearce said. "We need one or two new faces and it's my job to get them."
Fulham were inches away from scoring inside a minute when Rosenior skimmed a shot wide from a clear opening. Simon Elliott then forced James into an excellent tip-over with a ferocious 25-yarder.
City had their best spell midway through the second period. Darius Vassell forced a smothering from Antti Niemi with a toe-poke following Antoine Sibierski's through ball. Micah Richards went close with a header that whistled inches wide from Albert Riera's corner but played a big part when the deadlock was broken in the 69th minute. He nodded across goal from Joey Barton's free-kick and Dunne swept into the roof of the net from eight yards.
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