The result eased the pressure on his manager Chris Coleman, who was delighted with the determination his side showed to earn all three points from a thoroughly entertaining match.
Fulham went into the game desperate for goals, knowing that if results went against them they could drop into the relegation zone.
Stuart Pearce's City began the afternoon aiming to climb to second in the Premiership table, but you would been forgiven for being unable to tell which side were the strugglers.
Fulham attacked from the kick-off and the home fans did not have to wait long before being rewarded with a goal from Malbranque.
The Frenchman celebrated his 150th game for the club with his first goal of the campaign - a simple tap-in from four yards.
Richard Dunne failed to control a routine ball over the top and as the ball squirted away, Luis Boa Morte was on to it in a flash. The Fulham captain scampered down the wing and squared the ball to the waiting Malbranque, who made no mistake.
Joey Barton rewarded Malbranque with an appalling challenge soon after and was lucky to escape with a booking when a red card would have been more appropriate.
Rather than sitting on their lead Coleman's men continued to tear into the visitors, only to squander a combination of excellent chances and gifts from David James in the visiting goal.
Their lack of cutting edge looked all the more expensive when Lee Croft equalised midway through the half.
Darius Vassell and Stephen Ireland combined to put Croft through and the youngster lifted the ball over the advancing Tony Warner with a delightful chip.
Fulham went into the break with a deserved lead after Malbranque grabbed his second against the club he has been linked with in recent weeks. Boa Morte sent him clear with a perfectly weighted ball that split the defence and the Frenchman sent James to ground with an exquisite drop of the shoulder, before skipping round him and stroking the ball into an empty net.
The hosts could have extended their lead, but James atoned for his shaky first-half display by producing magnificent blocks to deny Collins John and Brian McBride.
His opposite number Warner tipped Vassell's late header over the bar as Fulham endured a nervous finish as the visitors laid siege to their goal.
Bradley Wright-Phillips thought he had earned a share of the points when he netted with an excellent finish, only to be ruled offside.
Only a comedy of errors prevented Fulham from increasing the margin at the death when Malbranque, Heidar Helguson and Tomasz Radzinski combined to miss when it was easier to score.