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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.