Christian Benteke's first goal of the season was followed by a wonderful strike from Wilfried Zaha in a first half that Palace dominated.
Leicester's Wilfred Ndidi was sent off midway through the second period for simulation only moments after he entered the book for a foul on Ruben Loftus-Cheek.
Substitute Bakary Sako added further gloss to the scoreline in added-time, curling home via the post having been teed up by Loftus-Cheek as Palace broke away on the counter-attack.
Benteke nets first away goal for eight months as Eagles pounce on poor Foxes peformance
The Eagles had not won on the road since 23 April when they beat Liverpool 2-1, and Benteke's goal was the first time they had scored an away goal since the striker's double at Anfield. Benteke connected with Andros Towsend's cross and powered his header past Kasper Schmeichel on 17 minutes.
Roy Hodgson's side deserved their lead and had already gone close twice before. Jeffrey Schlupp, facing his former side, had driven a cross for Benteke who failed to convert just in front of goal, before Loftus-Cheek's effort was parried by Schmeichel.
Leicester were constantly thwarted by a Palace defence playing an unusually high line and their two central midfielders, Yohan Cabaye and James McArthur, blocked any route to an isolated Jamie Vardy. Riyad Mahrez was also allowed minimal space on the Foxes' right with Schlupp and Loftus-Cheek doubling up on Leicester's danger man at the earliest opportunity.
Palace scored their second five minutes before half-time and it seemed the luck that had previously evaded them away from home this season was coming all at once. Benteke did well to fight off a number of challenges before feeding Zaha, whose sublime step-over fooled Ben Chilwell, and he fired low to Schmeichel's right.
Zaha and Benteke were outstanding throughout. Zaha's menace and trickery perfectly complemented his strike partner's hold-up play and the partnership is finally showing signs of fruition having been persevered by Hodgson.
Leicester improved in the second half but their only real contribution to the game was a disallowed Vincent Iborra goal. The midfielder had pushed James Tomkins before meeting an inviting free-kick and heading into the corner.
The game was effectively settled when Leicester were reduced to ten men following Ndidi's red card. The midfielder could perhaps feel hard done by because his first yellow card, a foul on Loftus-Cheek, was harsh, but he then went to ground under no contact and was correctly sent off by Martin Atkinson.
Benteke was denied a second by Schmeichel's fine save, but the Dane could do nothing about the eventual third goal as Sako whipped a fine effort into the top corner in added-time.
Palace momentarily move into 14th thanks to their seventh game without defeat - a fine return given their troubles at the start of the season. They face bottom club Swansea City next week.
Leicester had won their previous four games before today and will look to bounce back against Manchester United next week, which follows their League Cup quarter final against Manchester City in midweek.