Arsenal defender Thomas Vermaelen
Martin Jol's team looked like creating a shock when Gunners defender Vermaelen put through his own net mid-way through the second half while attempting a clearance.
But the Belgium international redeemed himself eight minutes from full-time when he headed home his second goal of the campaign, stretching Arsenal's unbeaten run to 10 matches.
Arsenal manager Arsene Wenger made two changes for the game, with Laurent Koscielny and Gervinho dropping to the bench, while Johan Djourou and Andrey Arshavin came in from the team that defeated Borussia Dortmund.
Fulham had John Arne Riise back following the birth of his son and Bryan Ruiz was given his chance on the left wing, replacing Damien Duff, who had a calf problem.
Jol's side looked to use the counter-attack and Ruiz set up an early chance for Clint Dempsey, which was blocked. Bobby Zamora also fired over the crossbar after spinning around Vermaelen.
But Arsenal were creating the more dangerous attacks and Arshavin had a strike disallowed for offside when Robin van Persie sent him through.
Mark Schwarzer, who was once a target for Arsenal, clawed away an effort bound for the top corner from Aaron Ramsey when the Wales midfielder was slipped in by van Persie.
Schwarzer was in action again when he saved from Theo Walcott at the near post, and the England winger set up Ramsey to blaze over after an exciting run that saw him speed past Riise.
Before the break, Moussa Dembele found room on the edge of the penalty area when he received the ball from Ruiz, with his shot deflecting just wide off Vermaelen.
Dembele also had an effort saved at the near post following a sweeping counter-attack when Zamora flicked for Dempsey to carry the ball forward and set up his team-mate.
With the final touch of the first half, Arsenal defender Per Mertesacker headed just wide when he met a free-kick, and there was more frustration for the hosts after the interval.
Van Persie was sent through by Mikel Arteta and he got a shot on target, but Chris Baird was back on the line to hack clear.
Referee Mike Dean also turned down a penalty appeal when van Persie was bundled over in the area by Dickson Etuhu and Brede Hangeland.
Fulham punished them in the 65th minute when they took a shock lead.
Danny Murphy's diagonal pass found Riise cutting in from the left, with the full-back chesting the ball as he moved into the penalty area.
Vermaelen came across to clear but succeeded only in steering the ball past goalkeeper Wojciech Szczesny.
Schwarzer saved well from Djourou when he met a corner, but Arsenal were level with eight minutes remaining as Vermaelen redeemed himself.
Walcott crossed from the right and the Belgian's downward header bounced into the roof of the net.
Even so, it was still a frustrating result for Arsenal, who also had a penalty appeal turned down when Dempsey appeared to block with his arm in the closing moments.
Short link: