Leicester had a goal ruled out and saw Wilfred Ndidi sent off in the second half, as the 2015-2016 champions failed to force their way back into the contest.
The Belgium global took a spot-kick against the orders of manager Roy Hodgson and failed to score in the 2-2 draw at Selhurst Park last weekend.
The Belgian striker broke his duck with a trademark header from Andros Townsend's cross on the right to put Palace ahead on 19 minutes.
Palace came into the game having not scored a goal away from home all season but Benteke made further amends as he set up the impressive Wilfried Zaha to score, with Bakary Sako adding a late third.
Last week, Benteke - who should have allowed Luka Milivojevic to take the spot kick as the Serbian had scored a penalty earlier in the match - apologised to his team-mates and manager Roy Hodgson, admitting he had let them down.
Conceding at least woke the Foxes up and Benteke nearly gifted them an immediate equaliser, heading inches wide of his own goal.
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It was Palace's first away goal of the season.
Ndidi was sent off for two bookable offences in nine minutes, the first for a foul on Ruben Loftus-Cheek and a second for a dive in the area.
It ended Leicester's hopes of salvaging the game and Benteke, who also should have won a penalty after he was fouled by Marc Albrighton, was denied a second by Schmeichel's point-blank save with 10 minutes left.
Leicester City manager Claude Puel: "It was not our day, it was not a good game for us".
"It was not a good game for us and Crystal Palace deserved this result".
"We know that he is a quality player and the goal he scored is the sort of one he's going to score, and had it not been for a wonder-save by Kasper Schmeichel, he would have scored two today because he got in the positions well".
"If you say to me would I like Yohan Cabaye to keep working here with me, then of course the answer is "yes", he said.