City raced into a two-goal lead through Jack Grealish and Rico Lewis at the Etihad and three points looked in the bag.
But Palace staged an incredible comeback to claw back a point - completed by a last-minute penalty from Michael Olise.
Jean-Philippe Mateta had grabbed one back 15 minutes from full-time before the Eagles netted the last-gasp penalty.
City could have jumped a point behind league leaders Liverpool with a win but now remain fourth in the table.
Liverpool, Arsenal and Aston Villa are all above the Premier League champions - and now all have a game in hand.
READ MORE ON CITY
'Amazing' Ange Postecoglou tipped to succeed Pep Guardiola at Man City
Transfer news LIVE: Chelsea consider Ramsdale move, Newcastle want Man City star
But this is a huge blow to City, who will be wondering how they did not claim all three points on Saturday.
Grealish had put them a goal ahead in the first-half after dominating throughout the 45 minutes.
In fact, they controlled the match so well that they claimed an incredible Premier League record that had never been registered before.
Nevertheless, they could not stretch their lead past one goal - until Rico Lewis netted his first goal for the club in the Premier League on 54 minutes.
Most read in Football
Bournemouth vs Luton match abandoned after Tom Lockyer collapses
Newcastle's nightmare injury crisis gets worse as two stars limp off against Fulham
David Wagner calls for 'idiot' Ipswich fans to be banned after Delia Smith car incident
'Amazing' Ange Postecoglou tipped to succeed Pep Guardiola at Man City
But instead of closing out the match like they had been expected to do, they seemed to awaken Palace.
Mateta pulled one back for the visitors after a sleepy moment from Kyle Walker, who allowed Jeffrey Schlupp to steal in and cross low.
Even at 2-1, City would have considered themselves strong favourites until the final moment in the match.
In dramatic fashion, Phil Foden downed Mateta after he tried to dash past the England international.
Olise, who was linked with a move to City in the summer before signing a new contract with Palace, had nerves of steel as he placed his penalty past Ederson.