Gary Cahill admitted Chelsea's run of four defeats in five Premier League matches before beating the Eagles had damaged their bid to finish in the top four.
The Blues ran out 2-1 winners against their south London opponents to put themselves just two points off a spot in the Champions League postitions.
Willian’s low shot gave Chelsea the lead after 25 minutes before Martin Kelly’s own goal doubled their advantage.
Antonio Conte’s side missed a catalogue of chances to extend their lead and they were nearly made to pay when Patrick Van Aanholt’s 89th-minute goal made it a nervy ending the game.