Jack Grealish's injury time winner at the Hill Dickinson Stadium earned David Moyes' side a valuable three points, whilst putting an end to the Eagles' 19-game unbeaten run in the process.
The Everton loanee completed the late comeback just days after missing out on another England squad - he is still yet to feature in one under Thomas Tuchel.
Daniel Munoz's well-placed first half goal was enough to see Oliver Glasner's side 1-0 up at the break, just 45 minutes away from extending their impressive unbeaten run to 20 games in all competitions.
As the match slowly progressed it looked as though Palace would see the game through until the visitors' defence were caught sleeping just 15 minutes from time as Tim Iroegbunam was brought down in the area to give the hosts a lifeline.
Iliman Ndiaye stepped up and sent Dean Henderson the wrong way to bring the game to life. With just minutes left on the clock, the Toffees built up excellently from the right flank, working the ball into the box where Grealish was on hand to blast home a rebound to cause limbs in Merseyside.
Glasner has proven himself as a top manager over the past 18 months or so at Selhurst Park, with a 5-0 defeat to Newcastle back in April being their last competitive loss.
Since then, a goalless draw with Bournemouth led to some unforgettable results as the Eagles won two trophies, defeating both Manchester City and Liverpool - a further victory over the Reds was to come, as well as draws with both Arsenal and Chelsea.
This proves that even without stars like Ebere Eze and Michael Olise in their arsenal, they can still challenge the elite.
After this result, Everton fly up the table into eighth - level on points with Chelsea - while Palace will have dropped out of the top five if City beat Brentford in the 16:30 kick-off, however, they will remain just four points off league leaders Arsenal.
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