Palace once again gave a good account of themselves but, just like in meetings with Tottenham Hotspur and Manchester United over the past fortnight, they fell just short as Patrick van Aanholt's late goal proved nothing more than a consolation.
Brazilian forward Willian soon found his range, though, picking out the bottom corner via a telling touch from Kelly to make it five goals in his last six games.
Palace had managed to net in six consecutive away outings heading into this match, and they nearly extended that tally through Andros Townsend's sweeping finish from the edging of the box, picking out the roof of the opposition net.
A second Chelsea goal seven minutes after their first gave them more breathing space, with Kelly once again the unfortunate man.
Eden Hazard worked the ball through for Davide Zappacosta to hit goalwards and, after initially doing well to clear off the line, Kelly saw the ball come back off Hennessey and then off his own leg and over the line.
Chelsea used the remainder of the first half to attack at will, coming particularly close to netting a third 45 minutes in through Giroud, who could not beat James Tomkins on the line at the end of an impressive passing move.
Hazard, seeking the goal to take him level with Jimmy Floyd Hasselbaink in Chelsea's all-time scorers list, also had one ruled out when rightly flagged for offside after converting from a close-range rebound.
Both teams wasted good chances in an entertaining second half, starting with Alexander Sorloth two minutes after the restart when picking out the post once Andreas Christensen was caught in possession.
Tomkins then launched himself at the ball to keep out Willian's goalbound shot and Giroud was thwarted by the long legs of Hennessey from a Thibaut Courtois punt upfield.
Hennessey and Courtois were then needed to keep out Willian and Van Aanholt respectively, before a couple of chances came and went for Giroud.
The French striker, preferred to Alvaro Morata today, diverted a cross over the bar with his head and then hit the frame of the goal from 12 yards.
Morata came off the bench and fired in Chelsea's 11th attempt on target, which Hennessey was equal to, while Sorloth had a goal ruled out late on for a high boot from Jairo Riedewald in the build-up - a harsh decision.
Palace are specialists at scoring in the final 15 minutes, though, now doing so 10 times from their 28 goals this term, but Van Aanholt's low blast past Courtois was not added to in the remaining three minutes of added time.
CHELSEA (3-4-3): Courtois; Azpilicueta, Christensen, Cahill; Zappacosta, Kante, Fabregas (Pedro 88'), Alonso; Willian, Giroud (Morata 72'), Hazard (Bakayoko 88')
CRYSTAL PALACE (4-4-2): Hennessey; Van Aanholt, Tomkins, Kelly, Wan-Bissaka; Schlupp (Riedewald 75'), Milivojevic, McArthur, Townsend (Lee 81'); Sorloth, Benteke (Zaha 45')