It left Birmingham kicking themselves for giving away three points after they had gone ahead with a 51st minute own goal from Moritz Volz.
The result capped a bad week for Birmingham after they reluctantly allowed Robbie Savage to join Blackburn a few days ago.
There is little doubt Birmingham missed the industry and enthusiasm of Savage. His replacement Salif Diao had a quiet first outing after sealing his loan move from Liverpool and the Senegalese player appeared to be out of touch for long spells.
Following Birmingham's fourth successive Premiership defeat, manager Steve Bruce expressed his disappointment with the result.
He said: "The referee made a howler of a decision when he awarded the penalty when the lad was a yard outside the box.
"It's decisions like this which cost you dearly. With 14 minutes to go it killed us off.
"We lost our discipline for the second goal. You cannot allow Diop those sorts of chances. He had been heading everything all afternoon.
"He is very good in the air and we did not deal with him. Salif Diao had a competent debut. Overall he did okay when you consider he last played on Boxing Day."
Fulham boss, Chris Coleman, said: "We certainly didn't deserve to lose and we squandered some good chances.
"But we kept at our task and in the end got a result. A month ago we lost at home to Birmingham but now we are looking really good.
"I thought Diop had another outstanding game. Although he does not speak much English he is a great leader and a powerful character.
"He has been a key player in the last few games along with Lee Clark who also makes a big difference. Even when we were a goal down he was still pushing us forward and was as major reason why we emerged with three points."
The result hardly appeared likely when Birmingham took a 51st minute lead when Volz, under pressure from Emile Heskey, was unable to prevent himself putting the ball in his own net.
Following this goal Birmingham appeared to be heading for the double over Fulham but they were overtaken by a series of events in which Luis Boa Morte was involved.
A patient Fulham grabbed their 77th minute equaliser when veteran Andy Cole converted a penalty after Boa Morte was impeded by Damien Johnson.
The unfortunate Johnson then conceded another foul when he again fouled Boa Morte to earn the second booking of the game.
On this occasion Mark Pembridge provided an accurate cross from the left to find Diop jumping high above Martin Taylor to head home a vital winner.
All the late action was in sharp contrast to a dire goalless first half. The game came alive six minutes into the second period when Birmingham finally forced Fulham's defence to surrender.
Mario Melchiot worked a cross from deep on the right into the middle of the Fulham penalty area where Heskey saw his shot parried by Edwin Van der Sar against Volz and into the net.
Fulham's response came in the next minute when Cole flashed an angled shot over the bar, while in the next minute the industrious Boa Morte was rightly booked for diving in the penalty area.
Fulham were mundane in many aspects of their play. Boa Morte was always active, while Pembridge grafted hard in midfield and they were involved in the winner from Diop.
Pembridge's free-kick was headed home by Diop when he outjumped both Mario Melchiot and Taylor.
MAN OF THE MATCH: Papa Bouba Diop (Fulham) – Scored the late winner and had a strong overall game.