Chelsea move into the top four with the win while Palace suffer back-to-back defeats in the league.
Chelsea dominated possesion in the first half but were restricted to few clear cut chances due to Palace's resolute defending.
The hosts opened the scoring five minutes after the break when Chilwell reacted first to a rebound in the box and smashed the ball into the net.
Chelsea doubled their lead when Zouma converted Chilwell's cross with a looping header.
Chelsea were awarded two penalties in the space of five minutes late on and Jorginho scored them both.
"The first half was frustrating but we didn't really create enough," Chilwell told BBC after the match.
"At half-time we spoke about being a bit more creative and taking a few more chances in the final third and we came out sharp in the second half and scored four very good goals.
"The biggest plus from today -- scoring a four goals is great but a clean sheet is perfect for us going into the international break. It's a good sign of things to come."
Lampard made six changes to the team that salvaged a 3-3 draw after being 3-0 behind at West Bromwich Albion last weekend, four of them at the back as he gave league debuts to Chilwell and goalkeeper Edouard Mendy.
"First half we started well, we came off it a little bit," he told BT Sport. "We needed a bit more. It was great for us to get four goals.
"Just the urgency of our game needed more. We needed to get Ben Chilwell into the game. We can't allow Palace's back four to say dealing with Chelsea's front line was easy.
"Ben Chilwell was fantastic today. His ability to be so high up the pitch, and that's not a bad thing, and his great quality on the ball. The lads who have come in have all had issues so we need to give them time but Ben has shown what he's all about."