Diego Costa’s goal saw Chelsea go nine points clear at the top of the table.
Cesc Fabregas dropped to the bench for Chelsea with Nemanja Matic coming back in. Eden Hazard missed the win at Sunderland because of a knock and he also returned to the starting 11, in place of Pedro, who was one of the substitutes. Also on the bench was Kurt Zouma.
Palace, with only one win in their last 10 Premier League games, made two changes from the side that lost 2-1 at home to Manchester United on Wednesday as Joe Ledley and Jason Puncheon replaced Mathieu Flamini and Lee Chung-Yong.
The match kicked off with Wilfried Zaha seeing plenty of the ball. The Palace winger had the Chelsea defence backpedaling in the opening ten minutes. But Chelsea pushed back, with David Luiz driving low, but his shot being deflected wide on 15 minutes.
Jason Puncheon then pulled his effort wide of Chelsea‘s goal after a clever cross from Martin Kelly.
But it was Chelsea who went into a forgettable first-half with the lead courtesy of leading goalscorer Costa.
On 43 minutes, Costa had his 13th goal of the season. Eden Hazard played the ball to Cesar Azpilicueta who dinked his cross from 20 yards onto the head of Costa.
The Spaniard timed his run into the area to perfection and sent a looping header past Wayne Hennessey.
It was rough on Palace, who had shaded the half before Costa’s intervention.
The second-half kicked off with Yohan Cabaye hitting a superb half-volley to force Thibaut Courtois into an impressive save. Again, Palace were controlling the game, but failed to find a cutting edge.
Both Blues had a further shot each denied by Hennessey before Alonso struck the bar on 85 minutes.
From a free-kick, Alonso’s clever curler beat the Palace keeper but hit his crossbar.
It was last meaningful effort on goal from either team as Chelsea held strong to earn the three points from a scrappy game.
The result gave Antonio Conte’s team a club record-equalling 11th successive win.