Trent Alexander-Arnold drilled in an 80th-minute equaliser with his right foot to deny City a 24th successive home win in all competitions.
Newcastle, who are unbeaten in their last seven league outings, climbed to sixth on 20 points after 11 games
Victory pushed Arsenal up to second place with 24 points from 10 games, two behind Tottenham Hotspur.
Chelsea squandered a two-goal advantage to end up with a point.
Arsenal came into the match having not beaten City in the league since 2015, a run of 15 games -- their longest winless streak against a single opponent in league history.
Liverpool won 3-1 while Arsenal were held 2-2 by Spurs.
Declan Rice and Gabriel Jesus scored in stoppage time in a 3-1 win for the Gunners.
Mikel Arteta's side were held 2-2 by Fulham leaving the Gunners with seven points.
Both sides had a number of decent chances in the first half-hour with the best of them falling to Arsenal's Eddie Nketiah, who hit the post in the 29th minute
Arsenal won 2-1 against Forest while Newcastle hammered Aston Villa 5-1.