The Toffees have been embroiled in a closely-fought relegation scrap with Leeds United and Burnley. They headed into the game against Palace at Goodison Park in 16th, a point above 18th placed Leeds.
Frank Lampard's men got off to the worst start possible when Jean-Phillipe Mateta and Jordan Ayew gave Palace a deserved first-half lead.
But Everton produced a phenomenal comeback with Michael Keane kickstarting it with a fine finish in the 54th minute. Richarlison then equalled matters with his 10th Premier League goal of the season in the 75th minute.
Dominic Calvert-Lewin then sent Goodison Park into a frenzy with an 85th minute winner. The English striker pounced on Demarai Gray's cross to tap home with Everton fans invading the pitch to celebrate.
Lampard's men were facing the disgrace of being relegated for the first time since 1951. However, with a crucial win today, they have avoided relegation.
Here are some reactions from fans from a phenomenal night for the Toffees:
Frank Lampard's Everton stave off relegation with monumental comeback win
Many questions were raised over Frank Lampard's appointment coming off the back of an ill-fated reign at Chelsea. The former midfielder replaced Rafa Benitez who was sacked in January following disappointing results.
The English manager encountered a woeful start to life at Goodison Park, unable to take them up the table with the side sitting in 16th. A 6-0 thrashing at Tottenham Hotspur on March 6 even had many touting Lampard to get sacked.
Things looked ominous for the former Chelsea captain when Everton plummeted into 18th place in April. But the Toffees have shown improvement in the dying embers of the Premier League season.
Two impressive victories over Chelsea and Manchester United put the Merseyside outfit in good stead.
They have now confirmed their survival in the most dramatic of circumstances, with Lampard able to breathe a sigh of relief.
It will be interesting to see what the future holds for the Toffees under Frank Lampard with all eyes on the upcoming summer transfer window.