City had two goals disallowed and missed a number of early chances in a tense derby at the Etihad.
But the 3-1 win from the first leg proved decisive, with Pep Guardiola’s men edging home 3-2 on aggregate.
City fail to cash in on bright start
City started the game like they wanted to end the overall contest as quickly as possible.
Sergio Aguero almost opened the scoring on seven minutes as he met Ilkay Gundogan’s chip with his head only for David de Gea to push the ball around the post
In those early minutes, the Reds were on the ropes and just about clinging on and De Gea would come to the rescue again 10 minutes later after a smart interchange by Aguero and Raheem Sterling saw the former hit a low shot that was again turned around the post.
But in football, it’s all about taking your chances and United, who had offered very little in attack, inevitably scored with their first and only shot of the first-half as Nemanja Matic fired a low shot past Claudio Bravo after a free-kick had been only half-cleared.
That was the only goal of the opening period and gave the tie an edgier feel.
The tension was getting to the supporters which in turn was reflected in several uncharacteristic misplaced passes.
But on 58 minutes, City had a glorious chance to level when Kevin De Bruyne sent Sterling scampering clear, but after delaying his shot a couple of times as he cut inside, he eventually blazed his shot over.
Kyle Walker almost scored with absolute thunderbolt shot on 71 minutes but De Gea was again equal to it, beating it away at the last second.
Then Aguero chased down a Harry Maguire clearance, it fell to sub David Silva, but his decision to pass instead of shoot saw Gundogan dispossessed and the danger cleared.
Goal-scorer Matic’s night ended on 77 when his persistent fouling finally caught up with him and the referee gave him his marching orders with a second yellow card.
Aguero thought he’d levelled shortly after, but, just as Sterling’s effort in the first-half had been, the goal was ruled out for offside.
Wembley again for the Carabao Cup experts
City are back at Wembley again.
The new decade is only one month old but the Blues have started it the way they ended the last one.
Now a final on 1 March against Aston Villa is in the bag and a chance to claim the first silverware of the campaign.
Clearly, this is a competition Pep, the players and the City fans love – now the aim will be to win it for the third successive year.
Man of the Match: Bernardo Silva
Never stopped running, chasing back and lifting the home support.
Pep keeps everyone guessing (again!)
Was it a back five back four or back three?
For the second time against United this month, the boss played an anything-but orthodox defensive line-up.
Kyle Walker, Nicolas Otamendi and Joao Cancelo looked like a back three, but then Rodrigo dropped when United came forward and it became a four.
It is fascinating to watch live and, while Pep has never been afraid to try new things or players in different roles, it is making it night on impossible for the opposition to second-guess how City will play.
Which is, of course, the whole point!
Pep reaction: Boss happy to be back at Wembley
"Today we met an incredible top side with physicality.
"With Lindelof, Maguire, Shaw and how good they defend, with Matic and Fred.
"We created enough chances to score a goal and in knockout games that is the difference.
"In the end we concede, as usual, so few chances.
"The goal was a set-piece and the first time they shot on target.
"The second half they shot once and no more than that.
"I am really pleased. For the 180 minutes we played, in both games we were better. I am so satisfied with the way we played and with the problems we have in the back four, with the injuries we have.
"I’m very pleased to be in the final for a third year in a row."
City return to Premier League action on Sunday with a trip to North London to face Tottenham Hotspur (kick-off 4.30pm)