Liverpool, having earlier beaten bottom club Fulham 2-0 at Anfield, will go into the international break in second place after receiving a favour from neighbours Everton, who held Chelsea to a goalless draw at Stamford Bridge.
Meanwhile, Arsenal had to come from behind to extend their unbeaten run to 16 games in all competitions with a 1-1 draw at home to promoted Wolverhampton Wanderers.
Man City moved on to 32 points from 12 games, while Liverpool have 30 and Chelsea 28, with all three teams retaining their season’s unbeaten record in the league.
City were on top from the start against a United team missing the injured Paul Pogba.
David Silva scored the first goal after 12 minutes and Sergio Aguero added a second soon after halftime.
Jose Mourinho’s side barely threatened until substitute Romelu Lukaku came on to win a penalty that Anthony Martial converted just before the hour mark.
But despite City largely controlling the game, it took a late third goal by their substitute Ilkay Gundogan to ensure there could be no repeat of United’s dramatic comeback to win 3-2 in the same fixture last season.
United remain eighth and are 12 points behind the leaders.
There was controversy at Anfield earlier after Liverpool took the lead against struggling Fulham just before halftime.
The London side felt that their Serbian striker Aleksandar Mitrovic should not have been given offside as he headed home and that goalkeeper Alisson took the subsequent free kick when the ball was moving.
Less than 15 seconds later from a lightning Liverpool break, it was in the net at the other end, put there by Mo Salah.
Xherdan Shaqiri scored a fine second goal, after which the heart seemed to go out of a Fulham team who remain bottom of the table with only one win from their 12 games.
“In this country, normally you cannot show disrespect to the referee and this is a problem because it’s shown disrespect to my team, myself and Fulham supporters,” said their manager Slavisa Jokanovic.
Chelsea’s manager Maurizio Sarri set a record in the Premier League era by completing his first dozen games without a defeat, but he would have expected more than a goalless draw from the home game with Everton.
His team failed to score for only the second time in the league this season against a well-organised Everton, who stayed ninth in the table.
“Of course, I prefer the three points today than the record,” he said.
In Sunday’s other game Arsenal fell behind to Wolves with a first half goal by Portuguese international Ivan Cavaleiro and did not equalise until four minutes from time through Henrikh Mkhitaryan.
The draw left Arsenal, fifth on 24 points, three points behind fourth-placed neighbours Tottenham, who beat Crystal Palace on Saturday.
