However Palace grabbed a goal back within two minutes through Yohan Cabaye and the comeback was complete 16 minutes later when Christian Benteke climbed above Yohan Benalouane, legally in the eyes of the officials, to head in Andros Townsend's cross.
Leicester's next league match is against Arsenal on April 26.
Crystal Palace have won five of their last six Premier League matches (L1).
It took only seven minutes of the second half for Leicester to double their lead, and demonstrate why their manager Craig Shakespeare has succeeded since replacing Claudio Ranieri.
Crystal Palace (4-2-3-1): Hennessey; Ward, Kelly, Sakho, Schlupp (Van Aanholt 67); Cabaye, Milivojevic; Townsend, Puncheon, Zaha (McArthur 84); Benteke.
Five successive league victories - a run that was brought to an end at Everton last Sunday - may have eased concerns Leicester might get drawn into the bottom three but Shakespeare's team selection suggested the manager would not allow a meeting with a team sat two points below the current champions to be overshadowed by Tuesday's tie.
Crystal Palace signed the versatile player from Leicester for £12.5m in January, although the Ghanaian has struggled to hold down a first team spot since.
Sam Allardyce gives huge update on Mamadou Sakho's contract situation with Liverpool
Shakespeare worked with Palace boss Sam Allardyce during Allardyce's 67 days as England manager. Belgium global Adnan Januzaj is set to depart Old Trafford in the summer for pastures new.
However, the club are hopeful that he will return to the side on Tuesday with Leicester going through a bit of a centre-back crisis at the moment.
Indeed, this is the first time Leicester have won three in a row against the Eagles in all competitions since March 1925 - they've never won four consecutively against them.
Crystal Palace took another step toward Premier League survival by recovering from two goals down to secure a 2-2 draw with Leicester on Saturday. What happens in the summer can only happen in the summer and can only be talked about, for me, when we are safe. "All I am concentrating on is making sure I stay focussed and the players stay focussed, and try to win every game we are in".
Palace talisman Zaha found it hard to get into the game at first, with Leicester crowding him out.
"I haven't seen the players this morning but I need to assess them all".
"Having seen him at very close quarters, he is diligent about the opposition, so it's no surprise to me", he said.
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