The Brazilian duly put the France 2018 FIFA World Cup winner on to score from close range.
Crystal Palace substitute Connor Wickham spurned the hosts’ best chance of the game when he toe-punted a shot over the bar in the dying minutes.
Chelsea remain in fourth place in the English Premier League, one point behind Manchester City — who were playing later on Sunday.
They are two points adrift of second-placed Tottenham Hotspur, but 11 behind leaders Liverpool, while Crystal Palace remain in 14th spot.
The win also gave Chelsea an important five-point cushion over Arsenal, their nearest challengers for the fourth UEFA Champions League spot who were hammered 5-1 by Liverpool on Saturday.
“It is never easy to play here or control it here, especially when they (Crystal Palace) play long balls, but we did well.
“We could have scored early but they also did a great match defensively, which is why it was so difficult,” Chelsea’s Luiz told reporters.
Chelsea forward Olivier Giroud had two goals ruled out for offside and then was forced off injured.
Coach Maurizio Sarri said the Frenchman had an ankle problem which looked set to rule him out of Wednesday’s game against Southampton.
This adds to the team’s fitness problems, particularly in attack with Pedro, Cesc Fabregas and Ruben Loftus-Cheek also currently sidelined.
“We played against a dangerous opponent. So, we had to have possession. We played well in the first 45 minutes and even better in the second half.
“The only thing I didn’t like is that we didn’t kill the match off,” added the Italian.
“That meant it was hard to defend the match in the box in the final minutes.”(Reuters/NAN)
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