The pivotal moment in the game arrived after 12 minutes when Steven Sidwell caught Mikel Arteta on the shin to receive the first dismissal.
Fulham responded well to the numeric disadvantage but they were caught out just before the break when Per Mertesacker headed home from close-range after Laurent Koscielny nodded on Theo Walcott’s free-kick.
The home side continued to ask all the questions in the second half and the finale became even more frantic when Olivier Giroud received a straight red card in the dying minutes.
Despite incessant Fulham pressure, Arsenal held on for a crucial victory that lifts them back to third, five points above fifth-place Tottenham.
However they play the first of their games in hand at home to Manchester City on Sunday, while Chelsea visit Liverpool.
At this rate, it is going to be tight to the end.
Wenger freshened up his side in response to the draw against Everton on Tuesday. Nacho Monreal replacedKieran Gibbs at left back while Tomas Rosicky returned in place of Jack Wilshere.
The England midfielder had been starting games despite a lack of match sharpness and, according to his manager, he had suffered a knock in midweek.
Fulham were safely ensconced in mid-table and had pushed Chelsea for 30 minutes before falling 3-0 here on Wednesday.
Arsenal would hand the initiative to Chelsea and Tottenham if they failed to win this afternoon but they began with all the intensity they displayed against Everton on Tuesday night.
Wenger’s men went for early goals. Walcott fired home and Koscielny headed over, though both were flagged offside.
However, in the 11th minute, the game changed complexion. Arteta prodded the ball away from Sidwell on the halfway line and the Fulham midfielder caught the Arsenal captain on the shin. Referee Andre Marriner did not hesitate in showing the red card.
The Fulham fans were unhappy but replays proved the referee correct.
Yet the home side responded well to their deficit. In the 20th minute, Urby Emanuelson broke clear and Koscielny’s slip allowed Dimitar Berbatov space on the right. The Bulgarian fired towards the near post but Wojciech Szczensy batted the ball away.
Then Alexander Kacaniklic burst through and his drive deflected wide off the foot ofPer Mertesacker and, after that, Kieran Richardson blasted wide.
Arsenal had taken time to adjust but gradually they began to look more threatening.
Just past the half-hour, Cazorla fed Giroud who swivelled on the edge of the area and fired an optimistic cross-shot towards the far corner. It bounced off the post and went wide to safety.
Emmanuelson robbed Monreal on the left and his low shot nearly caught out Szczesny at the near post.
Fulham had battled manfully but there would be a twist in the tail. Three minutes before the break Eyong Enoh clipped Aaron Ramsey and Walcott swung the free-kick to the far post.
Koscielny nodded it across the face of goal and, from a couple of yards out, Mertesacker nodded home his third goal of the season
It was a huge fillip just before the interval but, once again, Fulham responded well to adversity. However apart from an early free-kick by Bryan Ruiz, they never worried Szczesny.
Arsenal were happy to bide their time and keep passing the ball. But they also had to try and kill the game.
Wilshere and Lukas Podolski were waiting to come on when Fulham went close again. Stanislav Manolev’s errant cross forced Szczesny to tip over then, from the corner, Berbatov threatened at the far post.
Fulham were still going forward and, 13 minutes from time, had the ball in the net, when Szczesny spilled Richardson’s free-kick and Manolev stabbed home the rebound.
Fortunately for Arsenal the Bulgarian was flagged offside.
The home side were continuing to put the pressure on and the visitors were forced into some desperate defending.
Ramsey dragged a shot wide in the final seconds as Arsenal broke their shackles of Fulham pressure.
The final whistle was met with huge relief. This was a massive victory for Arsenal - and that is the most important thing.
But they will have to perform better if they are going to beat champions-elect Manchester United at Emirates Stadium next weekend.
