Robin van Persie returned to frustrate Arsenal as the Manchester United striker rescued a 1-1 draw at the Emirates Stadium, while Reading and QPR were relegated from the Premier League on Sunday after playing out a 0-0 draw.
Van Persie was making his first appearance in north London since last year's £24 million transfer to United and he was given a hostile reception from Arsenal's supporters.
But, after Theo Walcott gave Arsenal a second minute lead, the Dutch forward silenced the boo-boys when he fired home from the penalty spot after being fouled by Bacary Sagna in the 44th minute.
With the title already wrapped up, champions United were happy to settle for a draw, but the result was a setback for Arsenal, who dropped down to fourth place following Chelsea's 2-0 win over Swansea.
A win for either Reading or QPR at the Madejski Stadium would have kept alive their slender chances of staying up at least until Aston Villa's clash with Sunderland on Monday.
But both looked wracked with nerves during a goalless stalemate which condemned Nigel Adkins' Reading and Harry Redknapp's QPR to starting next season in the Championship.
At Stamford Bridge, Chelsea cruised to a comfortable victory over Swansea which lifted them into third place and one point ahead of Arsenal.
Rafael Benitez's side showed no signs of tiredness despite their recent gruelling schedule and Oscar gave them the lead with a fine finish from Frank Lampard's pass in the 43rd minute.
Lampard, who had come on as a substitute for the injured Ramires, netted the second goal in first half stoppage-time.
The England midfielder took his Chelsea career goal tally to 201 - within one of Bobby Tambling's record - when he drove home a penalty after Leon Britton had fouled Juan Mata.
That was enough to move Chelsea three points clear of fifth-placed Tottenham in the race to qualify for the Champions League.