"The first 20-30 minutes felt really strong from us. We were playing very aggressive and that drove us through the game," Pulisic said after the match.
Pulisic has scored just four Premier League goals this season but three of them have come in his last two matches
"There has been a lot of things going on this season but I will work hard to do my best in any way I can," Pulisic added. "I was happy I was able to do that today."
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.
"It was very good. We started very well, very aggressive and we had a high percentage of possession. We also had a good switch of play and we had a lot of touches in the box -- so a very good performance," Tuchel said after the game.
"We dropped a little bit after the third goal but we had a good response, especially after the goal we conceded. We created a lot of chances and didn't allow much for them."
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.
"[Havertz] maybe should've scored more, he had more chances," Tuchel added. "He can still improve his hunger and determination. He has outstanding quality. He's not the leader of this team and he doesn't have to be. He had excellent runs and he could've scored more."
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.