The hosts controlled the first half with Tammy Abraham twice going close.
Palace defender Mamadou Sakho headed wide from Andros Townsend’s cross shortly before half-time.
Chelsea went in front five minutes into the second half when Chilwell smashed in from the centre of the area.
Chilwell then crossed for Kurt Zouma to power in a header on 66 minutes.
Frank Lampard's side sealed their win with two penalties inside the last 12 minutes of play, both scored by Jorginho.
The first was awarded on 78 minutes when Tyrick Mitchell fouled Abraham. Four minutes later Sakho brought down Kai Havertz.
Chelsea’s win moves them up to fourth on seven points. Consecutive defeats drop Palace down to ninth.
Chelsea: 17 Oct v Southampton (H)
Crystal Palace: 17 Oct v Brighton (H)