Gary Rowett's side left Craven Cottage with all three points for the second year running after Clayton Donaldson's second-half penalty won the game for Blues.
Donaldson scored just after the break, dusting himself down after he saw an earlier spot-kick saved.
Rowett named an unchanged starting eleven after Blues' 3-0 win over Norwich City last time out.
In what was a blistering start to the match, Blues carved out the first chance of the game as early as the second minute; with Jonathan Grounds bursting forward, his low cross found Clayton Donaldson who was denied by a good block by defender Michael Madl - who was to have a 45 minutes to forget.
Fulham responded swiftly and were denied by both a great block and a great save.
Floyd Ayite firing an effort goalwards from the edge of the box which was superbly blocked by Michael Morrison, before Tomasz Kuszczak was on hand to deny Tom Cairney, tipping his curling effort over the bar.
Robert Tesche then went close, not once, but twice in a matter of minutes.
The hosts failing to clear a Grounds long throw effectively, with the German unleashing a volley from the edge of the area, flashing wide of David Button's right-hand post.
Then, after being tee'd up by Jacques Maghoma, the midfielder tried his luck from fully 30-yards, only to be denied by Button who palmed the ball behind for a corner.
From the resulting corner, defender Ryan Shotton rose highest and saw his effort land just the wrong side of the post.
Both sides then settled down after what was a hectic opening quarter of an hour, and after 22 minutes, Che Adams will feel he could have tested Button better. After being put through by Jonathan Spector, Adams couldn't quite sort his feet out and his effort was easily gathered by the Fulham 'keeper.
Three minutes later and Adams was involved again, this time winning Blues a penalty after being bundled down by Madl - the defender picking up a yellow card in the process.
Up stepped Clayton Donaldson, but unlike his previous penalty vs. Norwich CIty, the striker saw his spot kick tipped wide by Button.
Tesche and Maghoma both went close from the resulting corner, but both saw their efforts blocked.
Fulham skipper Cairney then broke into the Blues box from midfield, but as he tried to cut back onto his left foot, Morrison was on hand to crowd out the captain and clear the danger.
Just before the break, the hosts were reduced to ten-men, Madl - who brought down Adams for the penalty - picked up his second yellow card, after Donaldson reacted quickest to an underhit pass, Madl bringing down the Blues number nine as he looked to break forward.
The sides went into the break level, Blues having had the better chances with Fulham now a man light for the second 45 minutes.
Blues came out for the second-half with purpose...
Three minutes after the restart, referee Tony Harrington pointed to the spot once again, another Blues penalty. Che Adams again brought down, this time by Ayite.
Again, up stepped Clayton Doanldson, but this time with a very different outcome, as he fired past Button to redeem himself after his earlier miss.
With the hosts struggling to cope with Blues, two minutes after Donaldson put Blues ahead, Maghoma flashed a free-kick inches wide of the post.
Blues continued to dominate proceedings, much to the disgust of the riled home fans and could well have had a third penalty when Donaldson was brought down by Tomas Kalas, this time Harrington waving away the protests.
With both Fulham and their home fans becoming more frustrated, Blues looked to double their lead. After a smart turn in the middle of the park from Tesche, he found Adams on the edge of the area but his effort was straight at Button.
Cairney then went close after an intricate, mazey run down the left, but his shot was deflected over by Morrison.
After 65 minutes, Rowett introduced one of his deadline day signings, Lukas Jutkiewicz came on for Blues' goalscorer Clayton Donaldson.
Fulham the had their best chance to pull level with little over ten minutes remaining.
Substitute Neeskens Kebano was denied by a well timed tackle by Kuszczak, but after a blocked clearance, the ball wasn't cleared properly and fell to Scott Malone ten yards out, his shot curled inches wide of Kuszczak's far post.
With Fulham pressing, trying to find a way back level, Blues broke through substitutes Greg Stewart and Jutkiewicz, with the latter firing a long range effort over the bar.
The aforementioned Jutkiewicz then went close again, this time rising highest from David Cotterill's corner, but he couldn't find the target.
As the 90th minute loomed, Blues again looked dangerous on the break as both Cotterill and Maghoma were denied by Button and Kalas to keep the hosts in the match.
In stoppage time, Malone again went close. A deep cross to the far post found the full-back, whose downward header didn't trouble Kuszczak.