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.
City boss Pep Guardiola made nine changes to his side, who are now six games without a win in all competitions – his worst run as a manager.
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.
Mourinho’s momentum shift?
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 only four changes and retain key names.
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.
But while Guardiola said the competition was his “lowest priority” before kick-off, Mourinho perhaps took the chance to shift United’s momentum.
The League Cup was the first trophy he won in England. The last two times United eliminated City in the competition they went on to win it in 1970 and 1976.