Juan Mata struck to win a tight Manchester derby 1-0 as United knocked out EFL Cup holders City to reach the quarter-finals.
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.
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.