Thomas Tuchel’s side were looking to bounce back from a shocking 5-2 defeat to West Bromwich Albion in their last Premier League game and cement their challenge for a Champions League spot.
Havertz, who hasn’t scored since Oct. 17, scored Chelsea’s first after just eight minutes. After the Crystal Palace defence initially cleared the ball from the box, Eberechi Eze attempted to work it out further but was dispossessed.
The ball fell to Havertz who hit a left-footed shot into the bottom corner.
Chelsea then won a free-kick on 30 minutes which Mason Mount pinged into the box and Zouma headed into the net.
Crystal Palace pulled a goal back on 63 minutes when Jeff Schlupp put a probing ball into the box which Benteke headed in from close range.
However, Pulisic put the game out of their reach on 78 minutes when he pounced on a rebounding ball and slammed it into the net.