After 17 previous failed attempts, Chris Coleman's Cottagers finally secured that elusive first Premiership triumph on their travels.
Yet it appeared unlikely after central defender Richard Dunne put City ahead with only 21 minutes remaining.
Dunne put his City team-mates to shame after they had missed a string of earlier chances.
It looked as though the Irishman's goal would secure back-to-back wins after Tuesday's victory at Aston Villa had ended a run of six successive league losses.
But in an incredible turnaround Fulham scored two late goals to make it an away day to remember.
Substitute Collins John put Fulham on level terms in the 84th minute before Steed Malbranque struck the winner in stoppage-time.
It had to be Malbranque who inflicted the pain and misery on Stuart Pearce, who had unsuccessfully tried to sign the French midfielder last summer.
And Malbranque continued his remarkable scoring spree against City with this his fifth goal in six appearances against them.
Fulham made the livelier start in pursuit of that first away victory.
With a modicum of luck in front of goal they might have been two goals to the good inside the opening 10 minutes.
Less than a minute had been played when striker Heidar Helguson pulled the ball back invitingly for Liam Rosenior to shoot narrowly wide when he ought to have hit the target.
New Zealand international Simon Elliott did so shortly afterwards only to see City keeper David James pull off a brilliant save to turn over his 25-yard drive.
City's most dangerous player was Antoine Sibierski who was preferred up front to £6million man Georgios Samaras.
Sibierski forced visiting keeper Antti Niemi into an early diving save before seeing two headers fly narrowly over the crossbar.
The Cottagers were forced into a change midway through the opening half when Zat Knight limped off injured.
And within a minute his replacement Philippe Christanval was fortunate not to give away a penalty following a clumsy challenge on Dunne.
Fulham remained the more dangerous side and late in the first half Brian McBride, Rosenior and Luis Boa Morte all had decent strikes at goal.
Sibierski should have given City the lead on the stroke of half-time but he shot straight at Neimi following a free-kick from Joey Barton.
City made all the running early in the second half as Darius Vassell had three half-chances, while a couple more fell to Sibierski.
But when City finally made the breakthrough it came from an unlikely source in defender Dunne, who smashed a shot into the top corner from six yards after Micah Richards headed Barton's free-kick back across the face of goal.
City ought to have sealed victory shortly after Dunne's goal, but substitute Samaras dragged his shot narrowly wide.
And how City paid for that miss as Fulham drew level with six minutes left when Boa Morte brushed past Richards and squared the ball for John to slot home.
That sparked a City onslaught and Samaras was denied by a spectacular headed goal-line clearance from Rosenior after he chipped keeper Niemi and looked certain to score.
There was further drama in stoppage-time as Fulham snatched a victory which seven minutes earlier had appeared impossible.
Boa Morte's diagonal ball released Malbranque on the right of the penalty area and he thumped an unstoppable shot low past keeper James.