John Stones' goal in the early stages of the second half - his first since 2017 - put the visitors in front before Fernandinho struck from distance with seven minutes left to secure City's passage to Wembley where they'll face Jose Mourinho's Tottenham.
The final has been pushed back to April in the hope that fans will be allowed to attend.
City have won the League Cup seven times, including the last three. They defeated Aston Villa 2-1 in March 2020.
On a night they paid tribute to former midfielder Colin Bell after his passing on Tuesday, City were the better team and deserved to go through.
United threatened at times but ultimately fell at the penultimate hurdle. Ole Gunnar Solskjaer's side lost three semi-finals last season. For Red Devils skipper Harry Maguire, it was his ninth defeat in the last four of a competition.
Tottenham booked their place at Wembley with a 2-0 win over Championship Brentford on Tuesday evening.
John Stones gives Man City the lead against Man Utd at Old Trafford- Sky Sports (@SkySports) January 6, 2021
:tv: Watch Man Utd v Man City live on Sky Sports Footballpic.twitter.com/g26ecbOB0s
Chosen for YouChosen for You
Most Read StoriesMost Read