The defeat leaves United with just four points from their opening four Premier League matches, while City maintain their perfect start to the campaign.
• Manchester United: No goals
• Manchester City: Erling Haaland 60'
United appeared to have a major advantage when Phil Foden was sent off in the 23rd minute after an altercation involving Bruno Fernandes, leaving City with 10 men for more than an hour.
Despite their numerical disadvantage, City remained disciplined and continued to pose a threat on the counter-attack.
The breakthrough arrived in the 60th minute. Josko Gvardiol delivered the ball towards Haaland, who finished to put City ahead.
The goal initially appeared to have been ruled out for offside, but VAR overturned the decision after determining that Manchester United defender Patrick Dorgu had played Haaland onside. The Premier League's explanation also concluded that Enzo Fernández, who was in an offside position, had not interfered with play.
United pushed for an equaliser but struggled to create clear opportunities despite having an extra player for most of the match.
Marcus Rashford and Kobbie Mainoo both struck the woodwork, while City goalkeeper Gianluigi Donnarumma produced an important late save to preserve his side's lead.
The defeat will be particularly frustrating for United manager Michael Carrick, who strongly questioned the VAR decision that allowed City's winner to stand. Carrick argued that Fernández's position and involvement should have resulted in the goal being disallowed.
For City, however, the victory demonstrated considerable resilience. They played more than an hour with 10 men and still secured three points at Old Trafford.
The result keeps City on a perfect 12 points from four matches, while United's difficult start continues with only four points from their opening four league games.
