United are temporarily back on the podium with 38 units, one length behind their neighbor (2nd) and six behind Arsenal, who travel to Tottenham on Sunday.
Already beaten by bottom side Southampton (2-0) in the League Cup on Wednesday, the Citizens were once again laborious in the first period, despite high ball possession.
Pep Guardiola’s coaching seemed to work when Jack Grealish, three minutes after coming on, opened the scoring with a header on Kevin De Bruyne’s first breakthrough into the opposing box (0-1, 60th).
But United, who had two good chances against by Marcus Rashford in the first half, found the resources to come back.
On an action where the referee fairly generously felt that Rashford, clearly offside, had not interfered in the action, although he had not stopped his forward run, Bruno Fernandes equalized ( 1-1, 78th).
Galvanized, the Red Devils forced the decision by Rashford, still ahead of the last defenders, but behind the ball from the center of Alejandro Garnacho (2-1, 82nd).
For City, who will face twice Tottenham and twice Arsenal, including once in the FA Cup, in their next six matches, a quick reaction is imperative.
Liverpool sinks again
Overtaken in all areas of the game by Brighton more and more attractive, Liverpool have been badly beaten (3-0) and can start to worry about their chances of playing the Champions League next year.
With 28 points in 18 days, the Reds slipped to 8th place, overtaken by their hosts of the day. They are 10 points behind Newcastle and 4th place which offers the last ticket for the C1.
More than the result, it is the way that worries because, as in the defeat at Brentford (3-1), Jürgen Klopp’s men hardly existed.
They fell to Seagulls who, since the restart, apart from a dramatic 4-2 loss to leaders Arsenal, have won four games 15-3 on aggregate.
After a first period ended in a flattering 0-0 for Liverpool, his rearguard, deprived of Virgil van Dijk, injured, gave in on a double from Solly March (48th, 53rd) and a last goal from Danny Wellbeck (81st) .
The next day, in a week, against Chelsea, will already look like a double or nothing between the two biggest disappointments of the season.
Everton and West Ham depress
The other matches of the afternoon concerned rather the bottom of the table and could have an important weight in the fight for the maintenance.
After having offered City in the middle of the week, Southampton chained a third success in a row, in all competitions, by winning 2-1 at Everton, who had nevertheless opened the scoring.
Still the red lantern, the Saints joined the number of points (15) the Toffees (19th) and West Ham (18th), beaten (1-0) by Wolverhampton (16th, 17 pts).
Suffice to say that the fate of Everton coach Frank Lampard, although publicly supported by the club owner this week, and David Moyes, on the Hammers bench, is clearly in the balance.