Juan Mata struck to win a tight Manchester derby as United knocked out EFL Cup holders City to reach the quarter-finals Wednesday.
The Spaniard pounced to drive low into the corner from Zlatan Ibrahimovic’s pull-back as United enjoyed their best spell early in the second half.
Paul Pogba had hit a post moments earlier as the game came alive in the second period, following a first half in which neither of the bitter rivals managed a shot on target.
Manchester City boss Pep Guardiola made nine changes to his side, who have now not won in six games in all competitions.
Their best chance arrived early on when Kelechi Iheanacho headed over from six yards, while second-half substitutes Raheem Sterling and Sergio Aguero made little impact.
Victory was United’s second in five matches, and only Jose Mourinho’s fourth win in 18 meetings with Guardiola.
Meanwhile West Ham reached the quarter-finals of the EFL Cup as they confidently dispatched Chelsea but their victory was marred by crowd trouble at London Stadium.
Plastic bottles and seats were thrown towards the end of the match as hundreds of fans were involved in ugly scenes.
Security was boosted for the high-risk derby and an alcohol ban imposed as part of a “robust policing plan” aimed at minimising crowd trouble, with West Ham’s new home dogged by disturbances this season.
Chelsea made seven changes to the team that thrashed Manchester United 4-0 on Sunday and paid the price against a cohesive and intense Hammers side.
A superb Cheikhou Kouyate header before the break and an 18-yard Edimilson Fernandes strike a few minutes into the second half secured West Ham’s cup progress before more than 45,000 fans.
Gary Cahill swept home from close range in injury time for a consolation at the end of an entertaining match.
In another match-up Sunderland manager David Moyes was sent to the stands as his side were knocked out of the EFL Cup by Southampton.
Southampton’s record £16m signing Sofiane Boufal scored with a stunning long-range strike to secure a place in the quarter-finals for the hosts.
Moyes was dismissed after referee Chris Kavanagh waved away Sunderland’s appeals for a late penalty.
The Scot’s only two competitive wins in charge of the Premier League’s bottom club came in the previous rounds of the competition.