Palace's defense survived a Chelsea onslaught at Stamford Bridge in the first half - the Blues recording 11 shots to zero for Palace at the break.
"At halftime the manager said we need to stay focused and the chances will come," said Tammy Abraham. He broke the deadlock soon after.
Abraham read the game well to beat Palace's offside trap in the 52nd minute and met a backheel pass from Willian before shooting low for his 10th league goal of the season.
Pulisic ensured Chelsea's sixth consecutive league win in the 79th with a header when Michy Batshuayi's shot was deflected and looped into the air.
"I think we deserved it in the end. We had a lot of chances," Pulisic said. "We want to be right up there at the top so we're just going to keep going."
Pulisic didn't get a Premier League start from August until Oct. 26, when he took full advantage with a hat trick against Burnley. He followed up a week later with a goal against Watford.
Chelsea manager Frank Lampard handed midfielder N'Golo Kanté his first league start since Oct. 6 in place of Jorginho, who was suspended. Kanté had injured his groin on international duty with France last month.
There was a first Premier League start for 19-year-old right-back Reece James, dropping captain César Azpilicueta to the bench. James put in a solid performance, especially against Palace winger Wilfried Zaha.
"It was a really good individual performance from Reece because Zaha is a big threat on the flanks and one-on-one," Lampard said. "It gives me more options."
Palace had to wait until the 86th for its only shot on target all game. Kepa Arrizabalaga in the Chelsea goal reacted well to get low and hold the slippery ball in heavy rain.
It was the 300th Premier League game as coach for Palace's Roy Hodgson, whose team showed good early-season league form but is now on a four-game winless run.
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