The Gunners trailed from the first minute and looked set to suffer a shock defeat until Robin van Persie's penalty and a last-gasp Alex Hleb strike completed a stirring comeback.
The late goals ensured Arsene Wenger's side repeated the trick they managed to perform at the Emirates Stadium so many times last term - conceding the first goal and coming back to win.
Arsenal could not have made a worse start to the match. Gael Clichy's pass back to Jens Lehmann appeared to be innocuous, but the German keeper slipped and David Healy nipped in to slide the ball home on his Cottagers debut.
When the Gunners hit back, Tomas Rosicky dragged a shot just wide after good play by van Persie and Hleb.
Emmanuel Eboue then set up Hleb whose effort was blocked by Zat Knight as Arsenal slowly began to get into the game.
Fulham could not be written off though, and Simon Davies almost added a second for the visitors on the break midway through the first half.
The outstanding Tony Warner, who was a last-minute replacement for Antti Niemi, who was injured his wrist in the warm-up, then made a smart stop to turn Rosicky's low drive away for a corner as the Arsenal pressure mounted.
Fulham had penalty appeals turned down when Cesc Fabregas appeared to clip Steven Davies' heels before Warner another Hleb effort with his legs as Arsenal's frustrations grew.
In first-half stoppage time Fabregas was one-on-one with Warner but once again the keeper blocked the Spaniard's effort.
After the break van Perse's free-kick whistled just past the post and Rosicky was again denied by Warner, but for all Arsenal's possession they appeared to have run out of ideas as the match entered the final six minutes.
But Kolo Toure was then barged over by Carlos Bocanegra and van Persie slotted his penalty high past Warner and into the net.
Hleb then grabbed a stoppage-time winner, rifling a shot past Warner in dramatic scenes after being set up by Fabregas.