Chelsea dominated the first half, with the lively Pulisic denied by Vicente Guaita, while Willian’s effort on the stroke of half-time was brilliantly blocked by former team-mate Gary Cahill.
The deadlock was broken on 52 minutes, Willian flicking the ball to Abraham, who beat Guaita for his 10th goal of the season, level with Jamie Vardy.
James Tomkins headed Palace’s best chance wide before Pulisic nodded in from close range with 11 minutes remaining for his first goal at Stamford Bridge.
Chelsea's sixth consecutive victory moves them five points behind leaders Liverpool.
Palace are 10th with 15 points.
Chelsea: 23 Nov v Man City (A)
Crystal Palace: 23 Nov v Liverpool (H)