With star striker Erling Haaland absent due to injury, Pep Guardiola’s side trailed to Elijah Adebayo’s goal late in the first half at Kenilworth Road.
But, after squandering a host of chances, City finally clicked into gear with two goals in three minutes after the break.
Bernardo Silva equalised and Jack Grealish bagged the winner to give City a much-needed first victory in five league matches.
After their lethargic 1-0 defeat at Aston Villa on Wednesday, which followed draws with Chelsea, Liverpool and Tottenham, City were in danger of falling out of the title race.
Liverpool’s win at Crystal Palace on Saturday had moved the leaders seven points clear of City.
But fourth-placed City responded with a gritty display to close the gap on Liverpool to four points.
City still have work to do to regain control of their bid for an unprecedented fourth successive top-flight title and Haaland’s fitness scare could not have come at a worse time.
Haaland, who had started all of City’s league matches this season, was sidelined with a foot injury that could impact his availability for the treble winners’ hectic Christmas schedule.
Everton continued to shrug off the impact of a 10-point Premier League deduction as victory over Chelsea took the Toffees four points clear of the relegation zone.
Abdoulaye Doucoure opened the scoring at Goodison Park before Lewis Dobbin’s first Everton goal imposed another damaging defeat on Chelsea boss Mauricio Pochettino.
Without the penalty for breaching financial rules, which Everton are appealing, Sean Dyche’s men would be four points above Chelsea in mid-table.
Pochettino shuffled his pack after a dreadful display in losing 2-1 at Manchester United in midweek.
But the Argentine is struggling to solve his side’s lack of a clinical edge up front, despite the club having spent £1 billion ($1.3 billion) on new players in the past three transfer windows.
Fulham ran riot for the second time in a week as they thrashed West Ham 5-0 at Craven Cottage.
Just four days after Fulham beat Nottingham Forest by the same scoreline, Marco Silva’s side turned on the style again.
Raul Jimenez opened the scoring to take his personal tally to four in five games having previously not scored a Premier League goal since March 2022 for Wolves.
Willian and Tosin Adarabioyo netted for Fulham before the interval, with a fine effort from Harry Wilson and a late tap-in from Carlos Vinicius completing the London derby demolition.
AFP