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.
13 - Willian has scored 13 goals for Chelsea in all competitions this season - his best ever return in a single campaign for the club. Samba.— OptaJoe (@OptaJoe) March 10, 2018
The early exchanges gave every indication Palace were in for a long day, as Chelsea wasted no time in piling on the pressure.
They somehow failed to take the lead in the eighth minute, though, as Olivier Giroud's scuffed effort from close-range went straight to Wayne Hennessey.
But the goalkeeper was helpless in the 25th minute, as Willian darted in from the left and saw his long-range effort deflect in off James Tomkins, finding the bottom-left corner.
And Chelsea's second soon after was even uglier from Palace's perspective.
Willian stepped over a pass on the edge of the area, allowing Eden Hazard to take charge and feed Zappacosta into the right side of the box, with the Italian's attempt hitting Hennessey and going in off Kelly in calamitous fashion.
They almost added a fourth on the stroke of half-time, but Tomkins made a brilliant intervention on the line to deny Giroud at the end of an exceptional move.
Palace almost pulled one back early in the second half, as Sorloth charged through on goal and blasted against the left-hand post.
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.
Key Opta Facts:
- Chelsea posted 27 shots in this game; their most in a Premier League game this season and since May 21 2017 vs Sunderland (28).
- Chelsea have now conceded just five goals in their last 10 Premier League games at Stamford Bridge.
- Crystal Palace have won just two points in their last seven Premier League matches (W0 D2 L5).
- This was the 10th game this season that Wilfried Zaha hasn't started for Crystal Palace in the Premier League – they haven't won a single point in any of these games.
- Willian has now scored 13 goals for Chelsea in all competitions this season - his best return in a single campaign for the club.
- Olivier Giroud posted an xG total of 1.81 in this game from seven shots – this is the most by a player that has failed to score in a game in the Premier League this season. Giroud’s xG total of 1.81 is also higher than every other team to have played in the Premier League today bar Leicester City (1.83).
- Patrick van Aanholt’s consolation goal for Palace was the 800th scored in the Premier League this season.