Chelsea and Manchester City both lost at home in the Premier League on Saturday.
Maurizio Sarri's men went down 1-0, thanks to a second-half goal from Jamie Vardy.
City had the chance to close the 4-point gap between themselves and leaders Liverpool, but suffered their first defeat at home this season.
The hosts took the lead through Ilkay Gundogan, but Palace replied with three goals from Jeffrey Schlupp, Andros Townsend and Luka Milivojevic.
Although Kevin De Bruyne pulled one back for the champions, it was merely a consolation in the end.