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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 Jason Puncheon was the next player denied by Courtois.
Shortly before the break, the game descended into chaos as, first, Cesar Azpilicueta was shown a straight red card for a reckless lunge on Mile Jedinak which provoked a melee involving players from both sides.
The disruption before the break could have unsettled Chelsea, but, just seven minutes after the restart, they extended their lead in sumptuous fashion.
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Fabregas exchanged passes with Eden Hazard and Oscar before setting himself to net his first league goal for Chelsea since his summer move from Barcelona.
Chelsea were at ease once their two-goal lead had been established and Palace rarely tested Courtois in the second half.
The Eagles, though, did get a late consolation when Campbell got the goal he deserved in second-half stoppage time, but Chelsea held on to re-establish their five-point lead at the top of the table.