Chelsea have now lost three of their first eight league games and fallen nine points adrift of leaders Manchester City.
A scrappy Cesar Azpilicueta own-goal handed Palace the lead in the 11th minute, but Chelsea levelled seven minutes later when Tiemoue Bakayoko headed in a Cesc Fabregas corner.
Palace's Wilfried Zaha, on his return from injury, restored the home side's lead with a close-range shot on the stroke of halftime, and a lacklustre Chelsea were unable to equalise.
"That was really enjoyable," Hodgson said. "I have just said to the players that they really deserve to drink in that victory, because we played the champions of England but came off the field today having deserved our victory."
Chelsea manager Antonio Conte admitted his side had been hampered by the absence of striker Alvaro Morata and midfielder N'Golo Kante and the loss of Victor Moses to injury midway through the first half.
"We started very badly and it was a very difficult day," Conte said. "But we need also to understand the situation and to continue to work, to find solutions despite our injuries."
(Reporting by Matt Westby, Editing by Ken Ferris and Ed Osmond)
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