Jose Mourinho backed his misfiring strikers ahead of Saturday's game and Fernando Torres responded by scoring his first goal since October to put Chelsea in front.
In-form Palace striker Marouane Chamakh scored his third goal in as many games to equalise, but Ramires notched his first Premier League goal of the season with a fine strike to restore Chelsea's advantage before half-time.
Palace have been resurgent under new manager Tony Pulis and had chances to get something out of the game, but Chelsea held on to secure a seventh win out of eight home games in the top flight and close the gap on leaders Arsenal to two points.
Defeat for Palace ensured they remain in the relegation zone, but Pulis will take plenty of heart from their display.
Petr Cech replaced veteran goalkeeper Mark Schwarzer as Mourinho made six changes to the Chelsea side that beat Steaua Bucharest on Wednesday night.
Crystal Palace left-back Dean Moxey (hamstring) was ruled out, so Adrian Mariappa came into the starting line-up.
Chelsea enjoyed plenty of possession early on and they were in front after 16 minutes, when Willian's shot from 20 yards out was tipped onto the post by Julian Speroni and Torres reacted quickly to pounce from close range.
The marauding Branislav Ivanovic almost doubled the home side's lead four minutes later as he burst into the penalty area and flashed a right-foot strike narrowly wide of the far post.
Palace responded and were level after 29 minutes when Chamakh produced a fine left-foot finish to guide home Joel Ward's cross.
Eden Hazard was a constant menace to the Palace defence and the winger cut in from the left to set up Ramires, who let fly from 20 yards out to put Chelsea back in front with a venomous right-foot strike 10 minutes before half-time.
Chelsea made a bright start to the second half and Willian raced away down the left then picked out Juan Mata four minutes after the break, but the Spain midfielder scuffed his left-foot shot wide.
Palace were posing problems for the Chelsea defence and Jason Puncheon produced some trickery to fashion a chance for himself, but Cech got down well to save the winger's right-foot strike.
Yannick Bolasie spurned a chance to equalise when he headed over the crossbar from 10 yards out, then Damian Delaney also headed over as Chelsea lived dangerously.
Torres almost gave Chelsea breathing space, but his right-foot effort was well saved by the agile Speroni after 74 minutes.
But Palace came close again three minutes later when Stuart O'Keefe was thwarted by Cech and Ivanovic produced some desperate defending to deny the substitute from the rebound.
Ramires should have made sure of it five minutes from time, but he fluffed his lines and Speroni gathered. Speroni then made a final double save to deny Andre Schurrle and Demba Ba in a hectic finale.
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