But Abraham calmly slipped the ball past keeper Vicente Guaita to open the scoring soon after the break following a delightful flick from captain for the day Willian.
Pulisic, who has now scored five goals in Chelsea's last three Premier League games, wrapped up the victory with his 79th-minute strike, heading in after substitute Michy Batshuayi's blocked shot bounced up for the United States worldwide.
Abraham's 10th league goal of the season unlocked the Palace defence after 52 minutes of resistance, before Pulisic sealed a sixth consecutive league victory for Frank Lampard's side with his fifth goal in three league games.
Pulisic has started every match in all competitions for Chelsea since then, scoring five goals and assisting once.
The Spaniard has been an ever-present for Chelsea over the past few seasons and prior to Saturday's game Azpilicueta had started the Blues' past 73 Premier League fixtures - the longest current run in the division of any outfield player. "I think we deserved it in the end".
"This is where we want to be", Pulisic told ESPN Brasil when asked about his side's league position after the game. "We want to be right up there at the top so we're just going to keep going".
It meant defeat for Roy Hodgson in his 300th Premier League match as a manager. He followed up a week later with a goal against Watford. Kanté had injured his groin on global duty with France last month.
They do however have four key men back from injury in Palace quartet Mamadou Sakho, Andros Townsend, James MacArthur and Connor Wickham.
In between, the lively Pulisic also saw an effort well smothered by Guaita after a classy run while Reece James, who was preferred at right-back to the dropped Cesar Azpilicueta, sent in several risky crosses.
"It's more that I've got two choices at full-back there and Reece has done well".
Palace had to wait until the 86th for its only shot on target all game.
And Lampard has admitted his decision came due to the form of James at a good time give the youngster minutes.