Leading 3-1 from the first leg at old Trafford, city pushed forward in search of a goal to place the tie to bed however could find no way past an inspired David DE Gea.
Instead, United put things back within the balance before half-time once Nemanja Matic place them ahead on the night with their first effort at goal.
United had created nothing in open play however city could solely half-clear Fred’s free-kick and Matic swept a powerful first-time strike past Claudio Bravo.
De Gea, who had brightly denied Sergio Aguero and Riyad Mahrez within the gap minutes, was finally crushed once Raheem Sterling turned in Kevin DE Bruyne’s cross, however the flag was already up for offside .
The scoreline made for an anxious atmosphere at Etihad sports stadium at the break and a lot of United probabilities followed within the last half, with Harry Maguire heading over and Anthony Martial bringing a low save from Bravo.
Sterling, still without a goal in 2020, had an opportunity to settle his side’s nerves and restore their two-goal cushion once he ran clear however dallied and eventually skied his shot.
More wastefulness from the home side followed, notably when the ball broke to substitute David silva in front of goal however he selected to square to Ilkay Gundogan instead of shoot.
It was only when Matic was sent off for his second booking with fourteen minutes remaining that city regained any kind of management of the game, and they were ready to see out the rest with none further scares to ensure their progress.
Pep Guardiola’s side are into the final for a 3rd sequential year and will go for their seventh EFL Cup win once they face Villa within the final at Wembley on 1 March.
Only Liverpool, who have won it eight times, have a much better record within the competition.