Frank Lampard's side got off to a horrendous start as they found themselves two down at half time, with some poor defending allowing Jean-Philippe Mateta and Jordan Ayew to net for Palace.
However, the home side were a completely different team in the second half - Michael Keane halved their deficit with a neat finish.
Richarlison's deflected effort levelled the scores before Dominic Calvert-Lewin's bullet header completed the comeback and ensured Everton will not be playing in the Championship next season.
And although he didn't get on the scoresheet, Dele Alli's impact was phenomenal, having played a major role in changing the course of the game and Everton's equaliser - talkSPORT commentator Matt Jones saying Alli "completely changed the game."
The result puts the Toffees four points clear of the relegation zone going into the final day of the season.
The pressure had been so unbearable for so long, hundreds of fans and smoke grenades spilled onto the pitch in celebration and, while it was short-lived and good-natured, referee Anthony Taylor and his assistants retreated behind a wall of police on the touchline.
There was another incursion by thousands at the final whistle and inevitably there will be consequences for Everton, but nothing as damaging as what was staring them in the face with 150 minutes remaining of their season.
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