Per Mertesacker's 43rd-minute header proved enough for Arsenal to climb provisionally above Chelsea into third place, with its task made easier by Fulham midfielder Steve Sidwell's red card in the 12th at Craven Cottage. Arsenal also finished with 10 men after France striker Olivier Giroud's late sending-off.
Sixth-place Everton's hopes of reaching the top four nosedived by losing 1-0 at Sunderland, which climbed six points clear of the relegation zone thanks to Stephane Sessegnon's winner on the stroke of halftime.
With Stoke beating next-to-last Queens Park Rangers 2-0 away and Norwich overcoming last-place Reading 2-1, the final relegation berth looks to be between Aston Villa and Wigan, which lost 2-0 at West Ham to stay third from bottom.
Villa visits runaway leader Manchester United on Monday, and a win for Paul Lambert's side at Old Trafford will finally condemn QPR and Reading to the drop. The doomed pair is 10 points off safety with four games remaining.
In Saturday's other matches, Newcastle earned a point in its fight for survival with a 1-1 draw at West Bromwich Albion and Swansea drew 0-0 at home to Southampton, continuing its struggles since winning the League Cup at the end of February.
With Chelsea and fifth-place Tottenham not in action until Sunday, Arsenal — seeking Champions League football for a 16th straight season — didn't waste a chance to put pressure on its London rivals.
Arsene Wenger's team made heavy work of it, though, with Fulham having more shots at goal and dominating much of the second half despite being down to 10 men for 78 minutes after Sidwell's studs-first lunge at Mikel Arteta. It was Sidwell's first game back from a three-match ban.
"It spoiled the game a bit but we fought like lions and had better chances than them," Fulham manager Martin Jol said.
Mertesacker's goal, from close range after central-defensive partner Laurent Koscielny headed Theo Walcott's free kick across the face of goal, failed to liven up a strangely subdued Arsenal and there were some tense moments at the end, especially after Giroud's red card in the 90th for a tackle similar to Sidwell's.
"We played with the handbrake on and tried to keep the lead without taking risks," said Wenger, who suggested Giroud was always likely to be sent off for his tackle in light of Sidwell's earlier red card. "We didn't give them enough problems — we lost pace and quality."
Arsenal is unbeaten in six league games since losing 2-1 at Tottenham on March 3, a result that appeared to have seriously dented its chances of the top four. Arsenal next plays Man United, which could clinch the title with a win at Emirates Stadium.
The fate of QPR and Reading could be sealed on Monday, although it is more likely to be next week when they are finally consigned to the drop after spending weeks on the brink of relegation.
Peter Crouch and Jon Walters scored at Loftus Road to end Stoke's seven-game winless run, and QPR manager Harry Redknapp is losing hope of staying up.
"It looks almost impossible, doesn't it? It would take a real miracle," Redknapp said.
Reading remains bottom on goal difference after goals by Ryan Bennett and Elliot Bennett in a 90-second span moved Norwich seven points clear of Wigan, whose traditional end-of-season surge has slowed up in recent weeks.
A 1-0 loss at Manchester City was followed by a defeat at West Ham, with Matthew Jarvis scoring the opener in the 21st when his cross crept in and Kevin Nolan grabbing his 100th career goal to seal victory in the 80th.
"Every game is must-win game," said Wigan manager Roberto Martinez, whose team is three points behind Villa. "You look at the amount of points we have and it is not enough."
The decision by Sunderland's owners to fire manager Martin O'Neill and replace him with Paolo Di Canio last month continues to look inspired as the maverick Italian guided the northeast club to a second straight win.
Just like last weekend in a 3-0 victory at Newcastle, Di Canio failed to hide his delight on the touchline as Sessegnon scored in the 45th minute for the only goal at the Stadium of Light.
"I was a footballer at many clubs and it isn't easy when there's a change," said Di Canio, the former West Ham and Celtic forward. "The players can smile now but 37 points is not enough.
"Today was a step forward but the main job is not done."
Cardiff, which secured promotion to the Premier League four days ago, clinched the title in the second-tier League Championship by drawing 1-1 at Burnley on Saturday.