Ledley pounced with a close-range header from a corner to win an end-to-end encounter on Saturday against a Leicester side whose best effort came in the first half when David Nugent headed against the crossbar.
An open game offered up plenty of chances for both sides, but it was Alan Pardew who left the happier manager.
His excellent record since taking over at Crystal Palace continued, as the visitors claimed a third league win in their last four outings.
Palace started brightly and their first chance saw Jason Puncheon fire in a free-kick from the right, but it was straight at goalkeeper Mark Schwarzer.
Dwight Gayle then laid the ball back for Wilfried Zaha – restored to the starting line-up as one of two changes, alongside Jordon Mutch - but his shot was blocked by Wes Morgan as Palace continued to dominate the early stages.
Leicester brought in five players, including Nugent, and he went close with their first attack of note when his shot was deflected for a corner.
Zaha, who made his return from Manchester United permanent before the transfer window closed, saw his cross deflected to the far post, where Paul Konchesky headed clear.
As Leicester responded, Riyad Mahrez’s free-kick looked harmless, but Nugent’s flick-on had to be headed out for a corner by Scott Dann.
Mahrez - straight back into the side after returning from Africa Cup of Nations duty with Algeria - brought a good diving save out of Julian Speroni with a shot across goal.
Leicester almost took the lead after 26 minutes when Mahrez swung over a corner and Nugent’s header came back off the crossbar.
Jeffrey Schlupp then controlled a cross and fired into the ground to bring another fine save out of Speroni with Leicester’s third good chance of the first half.
Under-pressure Palace saw Dann need treatment following a clash of heads with Morgan as half-time approached, but they made it to the interval level.
Palace brought on Brede Hangeland at half-time for the injured Dann and on-loan Yaya Sanogo replaced Mutch.
Konchesky’s angled shot forced Speroni into another save as Leicester continued their fight to beat the drop, before Sanogo beat Morgan to a long ball but instead of passing to Gayle he shot straight at Marcin Wasilewski.
Palace were ahead after 55 minutes though when, from the resulting corner, Hangeland nodded the ball back across goal and Ledley headed Palace in front from close range.
Ledley then almost undid his good work with a backpass that Nugent nipped in to latch on to, but Esteban Cambiasso could not control his cut-back and Palace held on to their lead.
With 25 minutes remaining, Schlupp was replaced by Marc Albrighton as Leicester manager Nigel Pearson looked for an equaliser.
Puncheon almost increased Palace’s advantage late on when he fired just past the post with a dipping left-foot shot from outside the area before Leicester mounted plenty of pressure in response.
They laid siege to the Palace box in the closing stages, but they could not breach the visitors' defence as Ledley’s header proved decisive.
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