Frank Lampard’s went into their match with Palace at Goodison Park knowing a win would see them clinch safety.
They were in all sorts of trouble at half-time.
Goals from Jean-Philippe Mateta and Jordan Ayew meant Everton trailed 2-0 at the break.
But they produced an incredible turnaround in the second 45 minutes.
Goals from Michael Keane and Richarlison meant the scores were level with 15 minutes remaining.
Dominic Calvert-Lewin then scored the winner in the 85th minute to complete the turnaround and ensure Everton will stay in the Premier League.
Demarai Gray swung a free-kick into the box and Calvert-Lewin found the back of the net with a powerful header.
It was absolute scenes as Everton fans ran onto the pitch to celebrate the late goal. Watch the moment below…
11/10 limbs from Everton fans after Calvert-Lewin's goalpic.twitter.com/OcDdtRdzyW— Sam Street (@samstreetwrites) May 19, 2022
Everton held on to complete a heroic comeback and there was another pitch invasion when their Premier League safety was confirmed.
Everton can now go into their final game against Arsenal at the Emirates Stadium knowing they are safe, regardless of the result.
Norwich and Watford are already down. The third team to be relegated will be either Burnley or Leeds United.
Burnley and Leeds are both locked on 35 points going into the final day of the season.
Burnley will welcome Newcastle to Turf Moor, while Leeds will travel to London to play Brentford.
The Clarets have a much better goal difference, meaning Leeds will have to better Burnley’s result to ensure their safety.