The Gunners had the run of the opening 45 minutes, with Laurent Koscileny validating their dominance after he powered home a header when totally unmarked in front of goal.
Fulham reversed the pattern in the second half, desperately searching for an equalizer. Bobby Zamora, Philippe Senderos and Bryan Ruiz, amongst others, failed to put the ball in the back of the net, before Steve Sidwell finally nodded home five minutes from time.
With the clock seemingly ran out, Bobby Zamora netted a winner in the last minute of stoppage time to earn his team all three points.
Arsene Wenger made two changes from the side that beat QPR 1-0 at the weekend, as Francis Coquelin came in to replace the injured Thomas Vermaelen, while Gervinho was recalled ahead of Andrey Arshavin.
Orlando Sa had to make do with a place on the bench for Fulham after his goalscoring exploits against Norwich, as Martin Jol opted to bring Bobby Zamora back into the fray after the striker recovered from an Achilles problem. Steve Sidwell was also in to bolster the midfield.
Arsenal enjoyed the better of the opening exchanges, with Aaron Ramsey testing Mark Schwarzer from the edge of the box, before Gervinho wildly volleyed over after a corner found him in solitude at the far post.
John Arne Riise should have perhaps found the lurking Zamora with his whipped first time cross after being slotted in down the left.
The deadlock was broken in the 20th minute when Ramsey’s deflected cross from the left-side of the box found Koscielny totally unmarked and the centre-half nodded home.
Moments later the lead should have been doubled, as the ball pinballed around the penalty area, with Gervinho and Ramsey both failing to send it over the line.
As the home side pushed for an equalizer, Bryan Ruiz went close with a mazy dribble and slotted finish that went just wide before tumbling to no avail in the box under a challenge from Alex Song.
Theo Walcott and Ramsey were both guilty of spurning chances from just outside the area for the Gunners before the referee blew for the interval.
Ruiz rifled into the arms of Szczesny as the teams re-emerged as Fulham started in a mood that suggested they would take the game to their visitors.
Genuine chances on goal came few and far between for either team though, with the flowing nature of the first half being replaced by a more fragmented game punctuated by niggling fouls and breaks in play.
Sidwell fizzed an effort just over the bar from 30 yards out on the hour mark before Clint Dempsey skewed one wide when he would have hoped to test Szczesny.
Danny Murphy’s freekick saw the Arsenal keeper come rashly off his line and if Philippe Senderos could have directed in target, the ex-Arsenal man would have drawn the Cottagers level.
It was all Fulham by this point and Zamora powered over Mertesacker to send Ruiz’s delightfully dug-out cross fractionally wide of the upright.
Ruiz looked certain to slam home the equalizer when the ball dropped to him about 10 yards out, though the Costa Rican could only slam his effort into the legs of Szczesny.
Johan Djourou then received his marching orders after earning a second yellow by hauling down Zamora when he was through on goal. From the resulting free-kick, right on the edge of the box, Stephen Kelly could only hit the wall.With five minutes to go, Fulham finally got the goal they long deserved, when Szczesny could only palm a corner onto the head of Senderos, who looped the ball back in for Sidwell to power home from a couple of yards out.
Remarkably, with just one minute of stoppage time remaining, the ball dropped to Zamora just six yards out and his scuffed, left footed volley wrongfooted Szczesny at the near post to send all three points to Fulham.