Hakim Ziyech scored a late goal to see Chelsea win on their return to Premier League action.
Thomas Tuchel’s side had looked short of ideas for much of the game, although did see Ziyech’s first strike chalked off after VAR intervention had adjudged him to be offside.
Ziyech kept his eye on a looping cross by substitute Marcos Alonso and calmly side-footed in the volley at the far post to give Chelsea the win that they had looked unlikely to claim for much of the match.
Palace limited the visitors to only a handful of opportunities including a 35-yard pile-driver shot by centre-half Antonio Rudiger in the 11th minute that Vicente Guaita palmed away acrobatically.
The hosts had their own chances with Wilfried Zaha and Michael Olise coming close to breaking the deadlock as Palace sought to catch the visitors on the counter-attack.
Chelsea, who last weekend won the FIFA World Club Cup and next weekend face Liverpool in the League Cup final, have struggled to get the best out of record signing Romelu Lukaku and he mostly cut a lonely figure once again.
The win left Chelsea seven points behind second-placed Liverpool who beat Norwich City and 13 points behind league leaders Manchester City who play Tottenham Hotspur later on Saturday. Palace sit in 13th place.
