The home side dominated but conceded an equaliser just before halftime when Benteke, sold by Juergen Klopp in August, scored from a cross by Yohan Cabaye. In the 74th minute the Belgian stooped to head in a corner and win the game.
Klopp's team stay third but are five points behind second-placed Tottenham Hotspur having played two games more.
Palace, who have recently beaten Chelsea and Arsenal, moved up four places to 12th and should now be safe from relegation after a sixth win in eight games.
(Reporting by Steve Tongue; editing by Ken Ferris)
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