A wonder goal from Jovan Kirovski sealed the win - but Birmingham were forced to hang on for the last 20 minutes after Darren Purse was sent off.
The defenderÂ’s red card still failed to dent a Blues rearguard in a ragged, often scrappy game marred by nine other bookings including the two that saw Purse see red.
City stunned Fulham when Kirovski's first goal for the club came after just seven minutes. The American exchanged passes on the edge of the box with Clinton Morrison before firing a delightful curler beyond the reach of Edwin Van der Sar.
Birmingham could have gone a goal down earlier in the game when Sylvain Legwinski's glancing header from a corner was cleared off the line by Damien Johnson, astutely positioned at the back post.
Birmingham were then grateful for Nico Vaesen who twice raced out of his box to clear from the onrushing Legwinski and again from the same player five minutes later after the Frenchman had left the City defence for dead.
Legwinski must have felt it was not his day when his seven-yard header in the 43rd minute beat Vaesen but not Purse - the second City player in the right place on the line.
Kirovski clearly felt it was his day when he attempted a 30-yard free-kick which just missed dipping under the crossbar three minutes after the break.
Fulham must have sensed they were out of luck when substitute Junichi Inamoto lasted only six minutes before limping off following a challenge from Olivier Tebily and after that chances for the Londoners were few and far between.
Vaesen beat out a Lee Clark shot in the 67th minute and then Legwinski just failed to connect with an overhead shot with only the keeper to beat.
Birmingham's one clear chance in the second half saw Morrison sprint 30 yards but his close-range effort was stopped by the legs of Van der Sar.
Birmingham settled for a game played almost exclusively in their own third after PurseÂ’s high challenge on Calum Willock reduced City to ten men but they hung on for the three points.