N'Golo Kante scored the only goal of the London derby early in the second half as the Blues made the most of dropped points by Tottenham Hotspur and Arsenal yesterday.
Palace's three-match unbeaten festive run ended with a whimper as they failed to register a single shot on target, and they could have been more soundly beaten had a couple of debatable offside calls not gone in their favour.
The Eagles had kept three successive home clean sheets in the Premier League prior to kickoff and proved difficult for Chelsea to break down during the first half.
Antonio Rudiger did engineer a half-chance for himself on 13 minutes with an unchecked run to the near post, but he could not trouble Vicente Guaita with a difficult header from Willian's free-kick delivery.
The visitors were largely limited to shots from distance as Olivier Giroud teed up Kante for a 25-yard shot which he dragged wide.
When Chelsea did break the Palace lines, the offside flag thwarted Giroud who thumped Jorginho's lofted pass into the bottom corner on the volley, only for replays to show that the Frenchman's strike should have stood.
The woodwork saved Palace twice in as many minutes towards the end of the first half, with Willian striking the base of the post with a dipping free kick.
Another long-range hit from the Brazilian moments later forced Guaita to push around his post for a corner, from which Ross Barkley made a run across the front post and flicked against the frame of the goal.
Palace survived until half time but fell behind six minutes after the restart as Luiz found the run of Kante, who brought down the chipped through-ball and squeezed his shot under the arms of Guaita from 10 yards out.
Wilfried Zaha was on the periphary for the whole match and without the influence of their talismanic winger, Palace were void of an attacking threat for much of the contest.
Roy Hodgson introduced Max Meyer and Connor Wickham, making only his third Premier League appearance in two years, off the bench but Chelsea looked the more likely to add to the score and may have done so had Giroud's luck not been out.
Another marginal offside decision on 73 minutes denied the striker what would have been just his second top-flight goal of the season, the finish again emphatic as he held off James Tomkins and blasted a shot into the roof of the net.
Not until the final five minutes did Palace push for an equaliser, with Zaha bending a shot high and wide, and Wickham failing to keep down a left-footed prod on the half-volley after being set up 12 yards out by a Tomkins knockdown.
With the victory, Chelsea go five points clear of Arsenal in fifth and within two of second-place Spurs.
PALACE (4-5-1): Guatia; Wan-Bissaka, Tomkins, Sakho, Van Aanholt; Milivojevic, Kouyate (Meyer 78'), McArthur, Schlupp (Wickham 69'), Townsend; Zaha
CHELSEA (4-3-3): Kepa; Azpilicueta, Luiz, Rudiger, Alonso; Jorginho, Kante, Barkley (Kovacic 88'); Willian (Emerson 82'), Hazard, Giroud (Morata 76')