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 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.
Guardiola and Kompany concerns

Guardiola said City must be "more clinical" after they ended the night without working David de Gea once - the first time they have not had a shot on target in a game since 2012.

City, who are top of the Premier League, had an early penalty appeal turned down when Michael Carrick tangled with Aleix Garcia.

The wholesale changes made for the tie may blur detailed analysis of just what is amiss in recent weeks, but a switch to a 4-4-2 formation after two league games where a back three was used perhaps shows Guardiola has not yet settled on the way forward at City.

He could also face more time without captain Vincent Kompany, who, making only his second start of the season, asked to be replaced at half-time because he was tired.

Kompany suffered a groin strain in September but has been dogged by thigh and calf issues, prompting his playing time to fall from around over 2,700 minutes in 2013-14 to 1,700 last season.

There were some positives for Guardiola as 19-year-old full-back Pablo Maffeo made made some key interventions but if City fail to win on Saturday they would be seven matches without a win, a dire run not endured since 2004.
Man of the match - Marcos Rojo (Man Utd)

What the managers said...

Manchester United manager Jose Mourinho on responding to Sunday's 4-0 league defeat at Chelsea: "We were on a good run of results but it was a big defeat - numbers that the history of this club doesn't deserve.

"When I'm in a club my heart belongs to the fans and I felt deeply for them.

"The reality is that I never had people like these ones. We lost 4-0 and they were supportive.

"Today the stadium was full of real support and it looks like the love people have for the club is bigger than bad results, bigger than three bad seasons. We must give something back."

Manchester City boss Pep Guardiola: "I'm proud of the young players and how they played.

"At that level you need to be more clinical with the last pass but it's difficult against United. We are happy. I want to try to win but now we'll focus on the next competitions."
The stats you need to know

    Since Juan Mata's debut in January 2014, only Wayne Rooney (58) has been involved in more United goals than the Spaniard (47 - 29 goals, 18 assists)
    Zlatan Ibrahimovic provided his first assist for United in his 14th game

What's next?

Manchester City travel to the side who have made fewer passes than anyone in the Premier League this season - West Brom - on Saturday and host Barcelona three days later.

United face Burnley at Old Trafford on Saturday and visit Fenerbahce in the Europa League on Thursday.