Germany defender Per Mertesacker headed the only goal at Craven Cottage two minutes before half-time against a Fulham side reduced to 10 men after 12 minutes when midfielder Steve Sidwell was sent off against the club where he began his career.
Sidwell had only just returned from a three-match suspension after a red card in his last match against Queens Park Rangers.
Arsenal also finished with 10 men after French striker Olivier Giroud was sent off just before the final whistle.
The only other match to affect the top six on Saturday was Sunderland's 1-0 victory over European hopefuls Everton with the winner coming from Stephane Sessegnon on the stroke of half-time.
Arsenal's win at Fulham was the London side's eighth from their last 10 league matches and even manager Arsene Wenger conceded they were below their best despite the vital victory.
"We had a positive first half but in the second half we became sloppy with our passing and played with less pace to our game," the Arsenal boss told the BBC.
"You have to give Fulham credit; they are a good side and they played very well. It became hard in the second half. We played with the handbrake on and tried to keep the lead without taking risks. We didn't give them enough problems. We lost pace and quality."
Sidwell was sent off early on for a late tackle on Arsenal's Spanish midfielder Mikel Arteta while Giroud went late in the game for a studs-up tackle on Bulgarian Stanislav Manolev.
Arsenal are now on course for a 16th successive season in the Champions League, although Chelsea and Spurs are still firmly in contention.
Sunderland manager Paolo Di Canio, who took over three weeks ago, has now guided the lowly Black Cats to two wins out of three and relative safety, while their victory virtually ends sixth-placed Everton's slim hopes of Champions League football.
The Merseyside club remain on 56 points with manager David Moyes philosophical about their chances of a top-four finish.
"We probably didn't deserve to lose the game but we didn't play well enough to win it. It was a poor game. I don't think now we can make the Champions League.
"Mathematically we still can, but I think it's unlikely the teams above us are going to drop points. What we'll do is see if we can reach the Europa League and keep pushing for that. We do our best to compete," he told the BBC.
TRAP DOOR OPENING
It was a bad day for the bottom three sides who all lost to move a step nearer the relegation trapdoor.
Bottom-club Reading (24) lost 2-1 at Norwich City, while Queens Park Rangers (24) were beaten 2-0 at Loftus Road by Stoke City (37) who moved six points clear of the danger zone.
Stoke's former QPR striker Peter Crouch opened the scoring in the 42nd minute before Jon Walters added another nail to the home side's coffin with a second half penalty leaving Rangers boss Harry Redknapp to give an unequivocal summing up.
