Victory would have moved Brighton level on points with fifth-place Manchester City ahead of its derby against Manchester United later Sunday. But the loss left Fabian Hurzeler's team ninth and without a win in four matches.
Palace went ahead in the 27th minute through Chalobah, and Sarr doubled the lead for the visitors in the 33rd.
Sarr scored his second in the 82nd before Marc Guehi's own-goal pulled one back for Brighton. It was Guehi's second own-goal in his last four games.
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James Robson is at https://twitter.com/jamesalanrobson
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AP soccer: https://apnews.com/hub/soccer
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