But Chris Wood's second-half strike could not prevent Leicester slipping out of the Championship play-off places.
The New Zealander plundered his 20th goal of the season as the Foxes twice came from behind to grab a point.
But Bolton's win over Middlesbrough saw them leapfrog City into sixth, while Palace's hold on a play-off spot also looks far from secure.
Danny Gabbidon put Palace ahead but City levelled before half-time through Andy King before Stephen Dobbie tucked away his fourth goal of the season for Palace.
But Wood denied Palace a welcome win when he latched onto a defensive error to fire home in the 73rd minute.
Palace went ahead in the 26th minute when Dobbie floated in a free-kick and defender Gabbidon swept in his first league goal since March 2005.
But Leicester pulled level in the 37th minute when a slick move involving Paul Konchesky and Lloyd Dyer ended with King curling in a fine equaliser.
Palace's pressure told in the 67th minute when Glenn Murray's lay-off found its way to Dobbie on the edge of the area and the former Swansea frontman tucked away a fine strike.
But six minutes later a slip by Damien Delaney allowed Wood to charge through one-on-one with Julian Speroni and he made no mistake to snatch a point.