Freddie Sears scored Town’s fastest goal of the season to set Blues on the way to a fourth succesisve away win.
The striker found the net after just 16 seconds and then played a major part in Brett Pitman’s winner just before the hour.
Ross McCormack sandwiched an equaliser in between but Blues had the better chances throughout in a sixth away win of the Championship season that keeps Mick McCarthy’s side in the Play-Off places.
Town stayed with the same side that beat MK Dons at the weekend, the only changes being on the bench with David McGoldrick ruled out with a hamstring problem and Kevin Bru and Tommy Oar returning to the squad after injury.
The 2000 strong Blue Army didn’t have to wait long to have something to celebrate, Sears racing through to beat Andy Lonergan for his sixth League goal of the campaign.
Daryl Murphy almost got in for a second soon after, Dan Burn clearing the danger as the hosts looked rattled by Blues’ blistering start.
Pitman then threatened to get in behind Burn, the defender clearing, Blues going even closer with Ainsley Maitland-Niles smashing a 20 yarder against the bar.
Sears forced two corners in quick succession as Town swarmed all over the Cottagers, Jonas Knudsen the next to test his luck from distance.
Against the run of play, McCormack got Fulham back on level terms on 14 minutes though, firing a free-kick into the bottom corner from 30 yards after Knudsen had been penalised.
Luke Chambers’ flick was just over from a corner as Town responded, Cole Skuse then releasing Sears who sent a left foot effort over the bar. McCormack doing likewise at the other end.
Christophe Berra did well to clear from Moussa Dembele as he challenged for Luke Garbutt’s cross, Skuse then testing Lonergan from the edge of the box.
Chambers almost got in from Sears’ pass, Jonathan Douglas firing wide from 20 yards as Blues continued to threaten, Lonergan then doing well to smother Maitland-Niles’ shot after a terrific run from the Arsenal loanee.
At the other end, Tommy Smith blocked the danger from Dembele inside the Town box as an entertaining first-half came to an end with honours even.
Bru replaced the injured Skuse at the break, Town a whisker away from repeating the start to the first-half, Murphy almost getting on the end of Smith’s header from Knudsen’s long throw.
Fulham hit back with a left foot strike from Alexander Kacaniklic over the bar, Chambers then robbing Dembele after a counter attack from the Cottagers.
The impressive Maitland-Niles couldn’t find the target from 20 yards as the efforts on goal started to tally up and on 57 minutes Blues were ahead again, Sears the provider, Pitman the converter at the near post for his seventh goal of the campaign.
Jamie O’Hara and Tom Cairney were replaced by Emerson Hyndman and Matt Smith midway through the second-half in Fulham’s first changes, Smith sending a header just wide with his first touch.
Pitman made way for Piotr Malarczyk soon after with Blues going five at the back, the giant Smith posing an obvious threat in the air, another header going just wide.
Sears, who was outstanding throughout, was inches away with a curler after cutting in from the left, Fulham then making a final throw of the dice with Cauley Woodrow replacing Kacaniklic.
Dean Gerken held firm to gather Garbutt’s wicked cross at the near post, Dembele’s shot deflected wide as the home side searched for an equaliser.
It didn’t come as the home side left the field to a chorus of frustrated boos and Town to a standing ovation from the vocal Blue Army.