City initially took charge with a two-goal lead, courtesy of Jack Grealish and Rico Lewis at the Etihad stadium.
However, Palace turned the game around, leveling the score with a last-minute penalty from Michael Olise.
The champions could have closed the gap to league leaders Liverpool with a win but now find themselves in fourth place.
Liverpool, Arsenal, and Aston Villa, are all ahead of City now, even with outstanding games.
Despite Grealish’s first-half goal and City’s domination, they couldn’t capitalize on their control of the match.
Rico Lewis added a second goal on 54 minutes, but Palace did not give up their fight.
Jean-Philippe Mateta reduced the deficit, capitalizing on a lapse from Kyle Walker. The dramatic turn around point happened when Phil Foden fouled Mateta, leading to Olise’s nerve-wracking penalty that secured a crucial point for Palace.