West Ham's hopes of a place in next season's Champions League were all but ended after a 1-1 draw at Brighton on Saturday, while Leeds thrashed Burnley 4-0 at Turf Moor in a match overshadowed by an ugly incident between Ezgjan Alioski and Dwight McNeil.
The Hammers are now five points adrift of the top four with just six left to play for after two late goals at the Amex Stadium.
Danny Welbeck dinked home the opener for Brighton with just six minutes to go with the visitors caught chasing a winner.
Substitute Said Benrahma levelled with his first Premier League goal three minutes later, but a point leaves David Moyes's men still in sixth.
"It's obviously horrible because we had the Champions League in our sights," said West Ham midfielder Declan Rice, who made his return from injury.
"We can't be relying on other teams to lose. We have to go out and win. We've drawn too many and lost a few."
West Ham only secured survival in their penultimate game of last season, but have posed an unexpected challenge for Europe and can still secure a place in the Europa League should they win their final two games.
"This season has been outstanding," added Rice.
"We learned to win ugly this year. It's been a rollercoaster but we can still finish on a high."
Brighton remain in 17th, but are already guaranteed a fifth consecutive season in the top-flight.
Burnley also secured their survival with victory over Fulham on Monday and looked like a side already looking forward to their summer holidays as Leeds ran riot to cement their place in the top half of the table in their first season back in the Premier League for 16 years.
However, the major talking point was a clash between McNeil and Alioski, which Burnley boss Sean Dyche said will be reported to the English Football Association
McNeil shouted angrily at Alioski after making a crunching challenge on the Macedonian.
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