Diego Costa scored the only goal of the game, heading home just before the break. It was the Spaniard’s 50th goal for the Blues and ensured they have won their last 11 fixtures in the league.
Antonio Conte’s men sit nine points clear of Liverpool and Arsenal in second and third place.
For Palace, it was their second straight loss at home, after they were beaten 2-1 by Manchester United in midweek.
Alan Pardew’s side are 16th and just three points above the relegation zone.