It was only the second time Mourinho's Chelsea has lost in the league at Stamford Bridge, leaving the champions eight points behind leader Manchester City.
For Palace manager Alan Pardew it was a third victory over Mourinho in less than two years, with the previous successes coming while in charge of Newcastle.
After winning at Chelsea for the first time since 1982, Palace has a five-point advantage on its London rival after four games.
Saturday's game came to life after Bakary Sako put Palace ahead in the 65th minute. Although Radamel Falcao leveled with his first Chelsea goal in the 79th, Palace was back in front inside two minutes through Joel Ward.
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