Yerry Mina snatched a point for Everton against Wolves as his 99th-minute equaliser stunned Molineux.
The 1-1 draw moves the Blues two points clear of the relegation places but the battle for survival is now out of their hands as Leeds United and Leicester City, who are two and three points behind respectively, play their games in hand on Sunday and Monday.
Hwang Hee-Chan opened the scoring inside 34 minutes and Wolves were seemingly heading toward three points until Mina bundled the ball over the line from Michael Keane's cutback with virtually the last kick of the game.
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Attention now turns to the teams below Sean Dyche's side. Leeds take on West Ham United on Sunday at the London Stadium with the hosts fresh off the back of booking their place in the Europa Conference League final after beating AZ Alkmaar.
Newcastle United's St James' Park plays host to Monday night's clash with Leicester, who are looking to make a late surge out of the drop spots.
With Southampton already relegated, here are the remaining fixtures of the teams still fighting to survive:
Everton - 17th place
Sunday, May 28 vs Bournemouth (H) at 4.30pm
Leeds United - 18th place
Sunday, May 21 vs West Ham United (A) at 1.30pm
Sunday, May 28 vs Tottenham Hotspur (H) at 4.30pm
Leicester City - 19th place
Monday, May 22 vs Newcastle United (A) at 8pm
Sunday, May 28 vs West Ham United (H) at 4.30pm
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