Graham Potter once again made several alterations to his Chelsea lineup, but after a promising start, the hosts soon found themselves on the back foot.
The Blues had to survive a few nervy moments as Palace pushed for an opener, before wrestling back control of the contest.
With new signing Mykhailo Mudryk watching on, the often-maligned Havertz should have done better with a free header, but could only guide his effort over the bar.
A flurry of late chances saw Thiago Silva and Lewis Hall come particularly close to finding a breakthrough, yet the game remained goalless heading into the break.
A hopeful Conor Gallagher appeal underlined Chelsea’s growing desperation after the break. The Blues were struggling for attacking fluency, bringing on Pierre-Emerick Aubameyang in an attempt to spark the match into life, and within five minutes of his introduction, they were ahead.
Havertz atoned for his earlier miss, this time directing Hakim Ziyech’s cross beyond Vicente Guaita, leaving the visitors with little over 25 minutes to find a response.
Havertz then had the chance to virtually wrap up the points with 10 minutes to play, yet his close-range header at the back post somehow missed the target.
Palace had come from behind to win on four separate occasions this season, but second-half chances were at a premium until the final minutes.
Ultimately, Chelsea held firm to go level on points with next weekend’s opponents Liverpool, albeit having now played a game more.
For the Eagles, it's a sadly familiar feeling, having now lost 12 head-to-heads. on the bounce. More importantly, a sixth defeat in seven PL games leaves Palace looking nervously over their shoulder.
Flashscore Man of the Match: Conor Gallagher (Chelsea)
