Pep Guardiola's champions dominated their match at the Etihad but two late goals from Roy Hodgson's men, including a stoppage-time penalty, could have a major impact on the title race.
Crystal Palace have been something of a bogey team for Guardiola since he arrived in England in 2016 -- they are one of only three teams to have won at the Etihad more than once, along with Manchester United and Chelsea.
The champions enjoyed nearly three-quarters of possession in the first half but had only Jack Grealish's goal to show for their dominance.
The England winger scored for the third league game in a row, sweeping home after being found by Phil Foden in the 24th minute.
City had the ball in the net again early in the second half after Julian Alvarez's free-kick found the net but the goal was ruled out, with Rodri deemed to be in an offside position.
However, moments later the home side did extend their lead, when Rico Lewis thumped the ball into the bottom left corner.
City seemed destined to move to within one point of Premier League leaders Liverpool but instead they collapsed in dramatic fashion.
The away side scored against the run of play to give themselves hope in the 76th minute when Jeffrey Schlupp shrugged off the attentions of the City defence and crossed for Jean-Philippe Mateta to poke home.
City fans faced a nervous last quarter of an hour and watched in horror when referee Paul Tierney pointed to the spot after Foden fouled Mateta.
Michael Olise made no mistake, slotting home in the 95th minute and boos rang around the Etihad at the final whistle.
Game abandoned
Struggling Luton took the lead against in-form Bournemouth when Elijah Adebayo rose highest to head home a corner in the third minute but Dominic Solanke levelled just before the hour mark.
But the game was halted midway through the second half as Luton's Lockyer received medical treatment after collapsing off the ball.
The defender, who also collapsed during the play-off final win against Coventry in May before undergoing heart surgery, was removed from the pitch on a stretcher surrounded by the medical team, and there was a standing ovation from the crowd.
After the players were taken off, the Premier League confirmed the match had been abandoned.
"The Premier League match between AFC Bournemouth and Luton Town FC has been abandoned due to a player medical incident," said a statement from the English top flight.
"Our thoughts are with Tom Lockyer and all players involved in today's match."
Chelsea returned to winning ways at Stamford Bridge against bottom club Sheffield United, winning 2-0.
Cole Palmer smashed Raheem Sterling's low cross into the net in the 54th minute and he turned provider just after the hour mark as Nicolas Jackson slotted home.
It was just their third Premier League home win in a tough season for the injury-ravaged team.
Newcastle claimed all three points at their St James' Park stronghold after two consecutive league defeats.
Teenager Lewis Miley found the bottom corner in the 57th minute, Miguel Almiron made it 2-0 and Dan Burn scrambled home late in the game to put the result beyond doubt.
Burnley face Everton later on Saturday, with Sean Dyche's men aiming for a fourth straight win.
High-flying Aston Villa and Arsenal are both in action on Sunday, when Jurgen Klopp's leaders face under-performing Manchester United.
