Juan Mata struck to win a tight Manchester derby 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 set up a home tie with West Ham.
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.
Former Chelsea and Real Madrid manager Mourinho said on Wednesday his life in Manchester is “a bit of a disaster”.
His words and United’s poor form created a sense that defeat at Old Trafford would prompt tough headlines, and Mourinho admitted recent displays influenced his choice to make just only changes and retain key names.
Guardiola said before the game that the League Cup was his “lowest priority”, but he has now gone six games without a win for the first time in his managerial career.
United, far from at their best, scored during their only spell of quality in the opening 10 minutes of the second half as Ibrahimovic – anonymous in the opening period – profited from Nicolas Otamendi’s missed header to square for Mata.
There remain areas of concern for United. Luke Shaw was constantly outwitted by Jesus Navas and again there was no place in the 18-man squad for £26m summer signing Henrik Mkhitaryan.
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