The reigning champions lost to Manchester United and Manchester City in their last two games, but things were rather more straightforward this time around and they should have claimed a more comprehensive win over Palace given the number of chances they created.
Chelsea were on top for most of the first half and attempted a total of 16 shots, though both of their goals had more than a hint of fortune about them.
The in-form Willian got the first, as his 25-yard effort took a deflection on its way in, before Martin Kelly put into his own net after a Davide Zappacosta shot caused problems.
Palace nearly halved the deficit just after the restart when Alexander Sorloth hit the post, but that proved to be one of few opportunities for the visitors, who slipped to a fourth successive league defeat.
Patrick van Aanholt grabbed a consolation in stoppage time but it mattered little in the grand scheme of things and Chelsea moved to within two points of fourth-placed Tottenham ahead of their trip to Bournemouth on Sunday.
The hosts responded by crafting another fine chance of their own – Willian embarking on a remarkable solo run, before exchanging passes with Giroud and seeing his eventual shot crucially blocked just in front of the goal.
Giroud was presented with an even better opportunity 23 minutes from time, but he could only hit the post from the middle of the box after Marcos Alonso’s cut-back, and the former Arsenal man was replaced by Alvaro Morata soon after.
Van Aanholt set up a grand finale by providing a neat finish after good play by Wilfried Zaha in the 89th minute, but it proved to be too little, too late as Chelsea held on.