Cesar Azpilicueta and Damien Delaney have both been shown red cards in a feisty first half at Selhurst Park, with the visitors leading 1-0.
Azpilicueta was shown a straight red card in the 40th minute for a reckless challenge on Mile Jedinak before Delaney was given a second yellow just three minutes later for tugging back Loic Remy.
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Oscar handed Chelsea a fifth-minute lead when he whipped a vicious free kick into the top corner from 25 yards which Julian Speroni couldn't keep out.
However, it was Palace who had more chances in the first half and in the absence of Diego Costa, Fraizer Campbell looked the most potent attacking threat for either side.
Even before Oscar's strike, he had been denied by Thibaut Courtois, and Campbell pounced on a poor Gary Cahill header shortly after the goal, but the forward lifted his effort onto the roof of the net.
Moments later, he beat Cahill for pace, but lacked the composure necessary in a one-on-one situation and blazed his effort wildly over the bar.
John Terry - who scored an own goal to gift Palace a 1-0 win in the corresponding fixture last year - saw a header cleared off the line at the right end of the pitch as the hosts almost went two goals down.
However, Courtois had to be alert at the other end to prevent Yannick Bolasie's miscued cross from dropping under the bar in the 26th minute.
Chelsea looked a shadow of the side that have stormed to the top of the league and were lucky to still be ahead by the time the two red cards were shown shortly before the break.
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