A second-half strike from N'Golo Kante was enough for Chelsea to beat Crystal Palace 1-0 in the Premier League and send them five points clear of fifth-placed Arsenal.
Chelsea had a goal disallowed for offside and twice hit the post in the first half at Selhurst Park, but scored the winner five minutes into the second period when Kante (50) rolled the ball past Vicente Guaita.
Crystal Palace rallied towards the end of the game, with Connor Wickham almost poking home in the 89th minute, but they could not find an equaliser.
Chelsea now have 43 points on the board - five ahead of Arsenal in fifth - while Crystal Palace remain in 14th with 19 points.
Crystal Palace: Guaita (6), Wan-Bissaka (7), Sakho, Tomkins (6), Van Aanholt (6), Schlupp (6), Milivojevic (7), Kouyate (6), McArthur (6), Townsend (6), Zaha (6).
Subs used: Wickham (5), Meyer (5).
Chelsea: Kepa (6), Azpilicueta (7), Luiz (7), Rudiger (7), Alonso (6), Jorginho (8), Kante (7), Barkley (6), Willian (7), Hazard (6), Giroud (7).
Subs used: Morata (4), Emerson (n/a), Kovacic (n/a).
Man of the match: Jorginho.
Chelsea had their first chance of the game in the 14th minute. Willian curled a free-kick into the area, which Antonio Rudiger met with a free header, but it looped into the arms of Eagles 'keeper Guaita. Not long after, Kante tried his luck from the top of the box, but it just whistled past the far post.
The visitors had the ball in the back of the net just before the half-hour mark, but Olivier Giroud was flagged for offside in a marginal call. Jorginho pinged the ball over the top for the striker, but as he slotted home on the angle, the flag was raised and the goal ruled out.
Willian went close with another free-kick in the 35th minute. His curling effort deflected off the crossbar before going wide, although a corner was given - to the dismay of the home fans - as Guaita did not touch the ball as he attempted to make a stretching save. From the corner, Willian tested Guaita, who did push it away this time, before Ross Barkley put a header onto the crossbar from a second delivery.
Crystal Palace made one change with Jeffrey Schlupp replacing Max Meyer. Chelsea made two changes as Ross Barkley and Olivier Giroud came in for Mateo Kovacic and Pedro. Alvaro Morata started on the bench.
Chelsea did find the net five minutes into the second half. David Luiz pinged a ball over the top for Kante, who got behind Patrick van Aanholt to collect before sending the ball rolling past Guaita, with the Palace goalkeeper getting a fingertip to the ball but not enough to keep it out.
Giroud had the ball in the net for a second time in the 74th minute, but he was once again penalised for offside in another tight call. Willian played him through and he hammered the ball home, but the linesman had his flag up and it was ruled out. Giroud got his foot caught under the body of James Tomkins as he struck and injured his ankle, which resulted in him being replaced Alvaro Morata not long after.
Crystal Palace looked the most threatening in the final 10 minutes and could have snatched a late equaliser in the 89th minute. Luka Milivojevic floated a free-kick into the area, which was headed down for Wickham by Tomkins. He controlled with his chest despite some tight marking from Rudiger and managed to get a toe to the ball but sent it just over the crossbar from close range.
Roy Hodgson: "I thought we worked as hard as we could work and we were playing a very good team who made it difficult for us to disturb their passing rhythm... I don't know if we could have done much more in terms of our approach to the game. We played against a very good side and they were much better than we were."
Maurizio Sarri: "I like that we were in full control of the match for 85 minutes. We moved the ball very well and fast, especially in the second half.
"I think we need continuity, in the results and the performances. We need continuity in motivation and, as a consequence, in determination on the pitch, because in the last months we had some difficulties to find continuity."
- Crystal Palace failed to record a single shot on target in a Premier League home game for the first time since March 2017 vs Watford.
- Chelsea have won three consecutive Premier League away games for the first time under Maurizio Sarri, last doing so in April under Antonio Conte.
- Only Tottenham (9) and Liverpool (8) have won more away Premier League games this season than Chelsea (7).
- Chelsea's N'Golo Kante scored his third league goal of the season - his best-ever return in a single campaign in the top five European leagues.
Man of the match - Jorginho
Although it was far from a vintage performance from Chelsea, Jorginho continues to show his importance to the side. He played some world-class passes, especially in the first half, and had the most passes of any players on the pitch.
With Kante going forward more often - and scoring - he pulled the strings in the middle of the park and did well to limit Crystal Palace's quick attacking players throughout the game.
Crystal Palace's next game will be on Wednesday January 2 when they travel to Wolves in the Premier League. Chelsea will host Southampton on the same evening.