A second-half goal from N'Golo Kante was enough to give Chelsea a hard-fought 1-0 win at Crystal Palace.
Chelsea enjoyed plenty of possession in a first half lacking clear-cut chances but the visitors did come close to scoring when Willian struck the post from a free-kick.
On 51 minutes, Chelsea made the breakthrough. A ball over the top from David Luiz found Kante, who took it on his chest before firing past Vicente Guaita.
A clever flick from Eden Hazard found Willian but he was denied by Guaita who reacted well to save his low shot.
Olivier Giroud had a goal ruled out for offside for the second time in the match and then had to be substituted after injuring his ankle.
A second consecutive away victory means Chelsea remain fourth on 43 points but are now two behind Spurs and five clear of Arsenal. Defeat leaves Crystal Palace 14th on 19 points.
See: Crystal Palace report | Chelsea report
Next fixtures
Crystal Palace: 2 Jan v Wolves (H)
Chelsea: 2 Jan v Southampton (H)