The Blues’ victory means they are now five points behind leaders Liverpool and level on points with second-placed Leicester.
Tammy Abraham’s 10th league goal of the season and Christian Pulisic’s header ensured the win against a resolute Palace side who barely got out of their own half during the first period.
And after dominating a goalless opening half, Chelsea finally made the breakthrough when Mateo Kovacic and Willian combined to release Abraham – with the forward stroking a right-foot effort into the bottom right corner from 10 yards.
James Tomkins missed a glorious opportunity to equalise for the Eagles, heading Luka Milivojevic’s right-wing delivery wide from six yards.
But Chelsea more than merited their win, with Pulisic wrapping up the points with a close-range header after Michy Batshuayi’s deflected shot fell into his path.
Palace’s defeat, their third in four games, leaves them 10th in the table.