The Blues, who had lost their two previous home matches against the Eagles, were 2-0 up within 32 minutes after Willian’s deflected strike and a Martin Kelly own goal.
Palace’s Wilfried Zaha returned from injury at the interval and was quickly involved as Alexander Sorloth hit the post.
Chelsea nearly extended their lead as a close-range Willian shot was blocked, Wayne Hennessey denied Eden Hazard and Olivier Giroud struck the woodwork.
But Palace rallied late on, Patrick van Aanholt halving the deficit.
Chelsea held on, though, to inflict a fourth successive defeat on Roy Hodgson’s side.
The Eagles remain 18th, one point from safety.
Chelsea: 1 Apr v Spurs (H)
C Palace: 17 Mar v Huddersfield Town (A)