Matt Ritchie's 80th-minute penalty completed a remarkable turnaround by Newcastle, which fell behind to a goal from Sergio Aguero inside 25 seconds. It was the quickest goal scored in the league this season.
Salomon Rondon canceled out Aguero's goal with a 66th-minute equalizer.
City's loss kept Liverpool four points clear of the champions ahead of its home game against Leicester on Wednesday. City has 14 games to make up what could be a seven-point deficit.
A fourth league loss of the season looked unlikely for City when David Silva slipped as he attempted to reach Raheem Sterling's cross but still managed to head the ball across the area to Aguero, who hooked home the loose ball from eight meters out.
Newcastle might have been level with 13 minutes gone when Ayoze Perez dispossessed full back Danilo and raced in on goal, only to drag his shot across goalkeeper Ederson and just wide.
It took a goal-line clearance by Fabian Schar to deny Leroy Sane a second goal for City after Kevin De Bruyne, Fernandinho, Silva and Danilo combined on the stroke of halftime, but Newcastle made it to the break without further damage.
The visitors resumed where they had left off with Sane drilling a 49th-minute cross just ahead of Sterling's run, while Martin Dubravka pulled off a fine reaction save to deny Silva after De Bruyne had picked him out with a sublime pass.
De Bruyne made way for Bernardo Silva with 25 minutes remaining minutes after surviving appeals for a second yellow card following a challenge on Ritchie. De Bruyne had been booked in the first half for taking a free kick too quickly.
He had barely reached the bench by the time Newcastle equalized, Rondon reacting quickest after Isaac Hayden helped the ball into the penalty area to volley past Ederson.
And it got worse for City when Fernandinho, turning after receiving a pass, fouled Sean Longstaff inside the penalty area and Ritchie stepped up to smash the resulting penalty past Ederson.
City has now lost after taking the lead against Crystal Palace, Leicester and Newcastle this season.