Chilwell marked his 100th appearance in the competition with his fifth goal to break the deadlock early in the second half and crossed for Kurt Zouma to double the lead 66 minutes in.
Palace have already beaten Southampton and Manchester United this season, but a run of five consecutive defeats to Chelsea and just two wins in 11 attempts at Stamford Bridge in the top flight was hardly encouraging pre-game reading.
Indeed, Edouard Mendy – making his first league start for the Blues – was largely untested in goal as the home side eased to a third win in six games in all competitions this season through a Jorginho penalty double.
It had looked like being a potentially frustrating contest for Chelsea, Timo Werner shooting straight at Vicente Guaita with one of their few chances of a disjointed first half.
Kai Havertz and Callum Hudson-Odoi, who is again being courted by Bayern Munich, were lively in the Palace half but created little for central striker Tammy Abraham.
So it was that Chelsea’s breakthrough came through an unlikely source, Chilwell smashing the ball past Guaita from six yards out after Mamadou Sakho had made a mess of an attempted clearance in the build-up.
Chilwell then turned provider for Chelsea’s second, Zouma rising highest to loop a header over Guaita from the England left-back’s cross, having missed arguably an easier chance from an earlier corner.
Jorginho made matters safe, slotting a penalty to Guaita’s left after Abraham had been tripped in the box by Tyrick Mitchell.
When Sakho felled Havertz, Jorginho was able to score an almost identical spot-kick with eight minutes left – but only after Cesar Azpilicueta had taken the ball off an angry-looking Abraham.
Chelsea host Southampton next in two weeks’ time, with Palace’s next outing a home game against Brighton and Hove Albion on October 18.