Chelsea pair Oscar and Cesc Fabregas scored the decisive goals as Palace were beaten by Jose Mourinho's league leaders at Selhurst.
After the Brazilian had netted a superb free-kick early on, both sides went into the break with just 10 men after Cesar Azpilicueta and Damien Delaney were dismissed within three minutes of each other, but soon after the restart Fabregas capped a fine team goal to seal the victors although Fraizer Campbell netted a consolation for the hosts with a minute remaining.
Neil Warnock's side started brightly and created a couple of dangerous moments within the first two minutes. A fine through-ball by Yannick Bolasie found Fraizer Campbell who forced Thibault Courtois off his line but the Palace striker couldn't find a way around the keeper, and then the two combined again when the winger crossed for Campbell but Azpilicueta managed to clear.
But six minutes in the Blues took their first chance of the game when Willian won a free-kick 25 yards from goal which Oscar swept beautifully into the top corner over the fully-stretched Julian Speroni to open the scoring.
However the Eagles were causing problems in the final third and when Joel Ward played a long ball over the top Campbell pressured Gary Cahill into a poor back-header, and latched onto it but couldn't get the ball to drop under the crossbar after knocking it over Courtois.
The striker was looking hungry and soon after he picked the ball up on the halfway line and despite having no support he managed to advance 40 yards surrounded by Chelsea defenders, and after turning Cahill inside out he flashed his shot across the face of goal.
Willian then saw a shot fizz over the bar before John Terry nearly netted a header at the Holmesdale end for the second season in a row but James McArthur was well positioned on the line to clear.
After a lull, the game suddenly sprung into life again seven minutes before the break. After Puncheon had forced Courtois into a sprawling save, Chelsea were reduced to 10 men when Azpilicueta steamed into Mile Jedinak with a poor tackle and referee Chris Pawson had no hesitation in showing him a straight red card.
But three minutes later Palace were down to the same number when Delaney was shown a second yellow card for a foul on Loic Remy and he too was given his marching orders.
However six minutes after the restart the league leaders wrapped up the win in superb style. Fabregas played a one-two with Eden Hazard before repeating the trick with Oscar, and that gave him a shooting opportunity which he casually rolled past Speroni at his near post to complete a fine team move.
The Eagles' day took another turn for the worse when McArthur was forced off with a muscle injury when he cleared in defence, and after that Chelsea enjoyed more than the lion's share of possession with Hazard was next to try his luck but blasted just wide as the Blues seemed to settle for a what they had.
There was a slight chance for Palace with 10 minutes remaining when Campbell played in Bolasie who had the goal at his mercy but Cahill made a brilliant last-ditch tackle to snuff out the opportunity, but he finally got the goal his performance deserved with a minute to play.
Substitute Wilfried Zaha got past Felipe Luis on the right and put the ball on a plate for the striker to score his third goal in his last four games from close range and set up a grandstand finish, but it was ultimately too little too late for Palace.
Palace: Speroni, Kelly, Hangeland, Delaney, Ward, Jedinak, Ledley (Mariappa 58), McArthur (Guedioura 69), Puncheon (Zaha 69), Bolasie, Campbell. Subs not used: Hennessey, Fryers, Gayle, Chamakh.
Chelsea: Courtois, Ivanovic, Cahill, Terry, Azpilicueta, Matic, Fabregas, Willian (Luis 42), Oscar, Hazard (Salah 86), Remy (Drogba 90). Subs not used: Cech, Zouma, Mikel, Solanke.