John Stones steered in Phil Foden’s free-kick to give Pep Guardiola’s side the lead early in the second half and Fernandinho fired in a 20-yard volley to seal a deserved victory and our place in the final, where we will meet Tottenham Hotspur.
A minute’s silence was held before kick-off in memory of Colin Bell, who passed away on Tuesday, and City’s dominant performance was a fitting tribute to a man widely regarded as one of the greatest players in the Club's history.
Last month’s Premier League meeting between the two sides was characterised by its conservative feel, but the shackles were released from the off for this cup clash, in which an end to end first half produced everything but the decisive breakthrough.
Within five minutes both teams had goals disallowed, Marcus Rashford straying offside before his saved shot rebounded off Stones into the back of the net, with Ilkay Gundogan also flagged for the same offence as he turned in Foden’s low cross.
United looked dangerous on the counter-attack and Zack Steffen was at full stretch to keep out Bruno Fernandes’ curling 18-yard effort, but with City reproducing the rhythm that yielded success at Chelsea, it was Guardiola’s side who enjoyed the greater control.
Kevin De Bruyne cracked the post with a 20-yard drive that had Dean Henderson well beaten before the visitors had a second goal ruled out for offside when Foden set off too early on his way to nutmegging the United goalkeeper.
The tempo dropped before the break, but Stones' struck five minutes into the second period after Foden’s centre evaded everyone in the United area.
His first goal in more than three years breathed new life into the contest and from there, City turned the screw.
A slick counter-attack finished with Sterling's header forcing a good stop from Henderson, before another break saw the United ‘keeper make a fantastic fingertip save to deny Mahrez from the edge of the area.
United’s midfield started to probe as they bid to get back into the game, but City blunted the host’s attack as Fernandes misfired with a couple of efforts from outside the area.
It was a slender lead, but City looked comfortable and even more so when Fernandinho wrapped up the victory in emphatic fashion seven minutes from time.
Anthony Martial and Aaron Wan-Bissaka combined to half clear a De Bruyne corner and the Brazilian was well placed to rifle a sweetly struck volley into the bottom corner to all but end United's hopes of a late fightback.
Pep guardiola: victory dedicated to colin bell
"It was a sad day for all of the Manchester city family. We are in the present now but the past was created by great players. He has a stand in the Etihad Stadium and was called the king because he was special. This game is dedicated to Colin bell. A great night for us and especially for Colin and his family."
Man of the Match - John Stones
Will no doubt have breathed a sigh of relief after Rashford was flagged offside following what would have been his own goal, but it was another fine performance.
Comfortably handled United's attack alongside Dias and came up with the all important breakthrough goal when the game was finely balanced.
City have now had 16 different goalscorers in all competitions this season, more than any other Premier League team.
What it means
City become just the second team in the history of the League Cup to reach four consecutive finals, after Liverpool, who did so between 1981 and 1984.
We'll face Spurs at Wembley Stadium on Sunday 25 April, following the EFL's decision in December to delay the final in the hope more fans will be able to attend.
City are back in action on Sunday lunch-time when we welcome Birmingham City to the Etihad Stadium for an FA Cup third round tie. Kick-off is at 13:30 (UK).
Our Premier League campaign resumes next Wednesday, 13 January, with a home game against Brighton and Hove Albion.
CITY: Steffen, Cancelo, Stones, Dias, Zinchenko, Fernandinho (C), Gundogan, De Bruyne, Foden, Mahrez (Rodrigo 79’), Sterling.
SUBS: Trafford, Walker, Jesus, Aguero, Mendy, Nmecha, Harwood-Bellis, Mbete.
UNITED: Henderson, Wan-Bissaka, Lindelof, Maguire (c), Shaw, Fred, McTominay (Greenwood 75’), Rashford, Fernandes, Pogba, Martial.
SUBS: De Gea, Bailly, Telles, Tuanzebe, James, Mata, Matic, van de Beek.