Match ends, Manchester City 3, Everton 1.
Manchester City 3-1 Everton (agg 4-3)
Manchester City clawed back a first-leg deficit to beat Everton and set up a Capital One Cup final date with Liverpool after a thrilling game at the Etihad.
Everton looked on course for Wembley when Ross Barkley's brilliant run and 20-yard shot added to their 2-1 advantage from the first leg in the 18th minute - but manager Roberto Martinez was left nursing a burning sense of injustice after an enthralling encounter turned on a controversial decision.
Fernandinho's deflected shot put City level on the night before the break but Everton still had the edge. That was until City substitute Kevin de Bruyne, who was later taken off with a serious-looking knee injury, turned home Raheem Sterling's cross with 20 minutes left.
Everton could not recover their composure and City, who had earlier hit the woodwork through Sergio Aguero and David Silva, sealed their place in the final on 28 February when the Argentine headed De Bruyne's cross beyond keeper Joel Robles.
It meant joy for City and bitter disappoint tinged with fury for Martinez and Everton.
Everton suffer injustice
This was arguably the biggest game of Roberto Martinez's reign as Everton manager, and a chance to silence criticism of his methods by setting up a League Cup final meeting with Merseyside rivals Liverpool.
And for 70 minutes Martinez and his team looked likely to pull it off, impressively standing toe-to-toe with City with a mixture of defensive solidity and threat on the break.
It was all turned on its head in a moment that will haunt and anger Martinez, as Sterling appeared to have run the ball out of play before crossing for De Bruyne to switch momentum decisively in City's favour.
The home side will not have sympathy for Everton in this context after being convinced Ramiro Funes Mori scored an offside goal in the first leg and that Jesus Navas was denied a penalty after he was fouled by Kevin Mirallas - but it was easy to understand Martinez's outspoken frustration.
City were increasing the pressure but Everton were surviving, with some good fortune, and that second goal stunned Martinez's team and gave the home side the push they needed to finally see Everton off.
Once more Everton never looked fully secure at the back but they certainly had a hard luck story to tell here.
Good news, bad news for Man City
Manchester City can now plan for a Wembley date with Liverpool, who beat them so comfortably 4-1 here at the Etihad earlier this season - but it was a night of mixed news for manager Manuel Pellegrini.
Aguero, whose season has been hampered by injuries, looked back to his blistering best and never gave Everton's defence a moment's peace, hitting the post with a superb curling effort then showing his world-class by heading in De Bruyne's cross for the goal that clinched City's victory.
The bad news is that injury to the brilliant De Bruyne, who had a huge impact after coming on as sub, scoring that controversial second and setting up the third.
The sight of the 24-year-old being taken off with his knee in a brace put a dampener on an exhilarating night and City will wait anxiously for the medical bulletin.
Barkley shows his class
Ross Barkley's run and finish that put Everton ahead in the 18th minute was more compelling evidence of a wonderful natural talent.
City simply could not cope with his movement and power when Everton had moments of superiority in the first half, and it was no coincidence that their effectiveness was reduced once he was subdued.
Barkley is occasionally the target for harsh criticism from a minority of Everton's fans, which sometimes subdues his sense of adventure - but it is clear they have a special player on their hands.
On a night of bitter disappointment for Everton, they can be consoled by the presence of the likes of Barkley, a player they must build around and secure for the future.
Man of the match - Sergio Aguero (Manchester City)
What the managers said
Everton manager Roberto Martinez on BBC Radio 5 live: "Everyone that has seen the replay can clearly see the ball is out of play when the ball is crossed in for City's second goal. The tie was a real good football game. You don't expect to concede a goal in that manner. It's very, very hard to take.
"City are a very good side. If they score three goals in the right way then you accept it. The first goal was a deflected shot, but for the second goal the ball was clearly out.
"We have a very good group of young players. I hope we take this display as inspiration."
City manager Manuel Pellegrini: "I am very happy to play a final at Wembley, it is very important.
"We deserved to be in the final, we had just one defeat - that was against Everton with a clear penalty.
"They scored for 1-0 and it was a clear foul. If you think because of that ball [Sterling to de Bruyne], that is not why we won.
"We won because we scored three goals and Everton had just one chance."
The stats you need to know
- Manchester City will now play in a major final for the fourth time in the past six seasons
- Sergio Aguero has scored five goals in his past three games for City in all competitions
- De Bruyne has scored five goals in five appearances in the League Cup this season, including at least one in every round
- City have found the back of the net in all but one of their past 27 home games in all competitions
City are away at Aston Villa in the FA Cup fourth round on Saturday, and Everton are at Carlisle in the same competition on Sunday.
- 30OtamendiBooked at 85mins
- 18DelphSubstituted forJesús Navasat 45'minutes
- 21SilvaSubstituted forFernandoat 80'minutes
- 42Y TouréSubstituted forDe Bruyneat 66'minutes
- 15Jesús Navas
- 17De Bruyne
- 5StonesSubstituted forColemanat 77'minutes
- 25Funes Mori
- 3BainesBooked at 89mins
- 15CleverleyBooked at 84mins
- 19DeulofeuSubstituted forKonéat 60'minutes
- 21OsmanSubstituted forMcCarthyat 60'minutes
- 10R Lukaku
- Martin Atkinson
- Shots on Target
Second Half ends, Manchester City 3, Everton 1.
Offside, Everton. Tom Cleverley tries a through ball, but James McCarthy is caught offside.
Offside, Everton. Leighton Baines tries a through ball, but Ramiro Funes Mori is caught offside.
Attempt missed. Arouna Koné (Everton) right footed shot from the right side of the box is too high.
Delay over. They are ready to continue.
Kevin De Bruyne went off injured after Manchester City had used all subs.
Delay in match Kevin De Bruyne (Manchester City) because of an injury.
Leighton Baines (Everton) is shown the yellow card for a bad foul.
Jesús Navas (Manchester City) wins a free kick on the right wing.
Foul by Leighton Baines (Everton).
Attempt missed. Sergio Agüero (Manchester City) header from the centre of the box misses to the left. Assisted by Kevin De Bruyne with a cross following a corner.
Corner, Manchester City. Conceded by James McCarthy.
Attempt blocked. Sergio Agüero (Manchester City) right footed shot from a difficult angle on the right is blocked. Assisted by Kevin De Bruyne.
Nicolás Otamendi (Manchester City) is shown the yellow card for a bad foul.
Foul by Nicolás Otamendi (Manchester City).
Arouna Koné (Everton) wins a free kick on the right wing.
Tom Cleverley (Everton) is shown the yellow card for a bad foul.
Fernandinho (Manchester City) wins a free kick on the left wing.
Foul by Tom Cleverley (Everton).
Substitution, Manchester City. Fernando replaces David Silva.
David Silva (Manchester City) wins a free kick on the left wing.
Foul by Gareth Barry (Everton).
Raheem Sterling (Manchester City) wins a free kick in the defensive half.
Foul by Seamus Coleman (Everton).
Substitution, Everton. Seamus Coleman replaces John Stones.
Goal! Manchester City 3, Everton 1. Sergio Agüero (Manchester City) header from the centre of the box to the bottom left corner. Assisted by Kevin De Bruyne with a cross following a corner.
Corner, Manchester City. Conceded by Tom Cleverley.
Attempt blocked. Fernandinho (Manchester City) right footed shot from outside the box is blocked.
Attempt blocked. Kevin De Bruyne (Manchester City) right footed shot from outside the box is blocked.
Fernandinho (Manchester City) wins a free kick in the attacking half.
Foul by Tom Cleverley (Everton).
Goal! Manchester City 2, Everton 1. Kevin De Bruyne (Manchester City) right footed shot from the centre of the box to the bottom right corner. Assisted by Raheem Sterling.
Jesús Navas (Manchester City) wins a free kick in the defensive half.
Foul by Tom Cleverley (Everton).
Foul by Gaël Clichy (Manchester City).
Arouna Koné (Everton) wins a free kick in the attacking half.
Offside, Manchester City. Jesús Navas tries a through ball, but Kevin De Bruyne is caught offside.
Martín Demichelis (Manchester City) wins a free kick in the defensive half.
Foul by Arouna Koné (Everton).