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.
Relive the action as it happened from the Etihad Stadium
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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.
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.
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.
Everton manager Roberto Martinez on BSports 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."
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.
Full Time Match ends, Manchester City 3, Everton 1.
90:00 +7:43 Full timeFull Time Second Half ends, Manchester City 3, Everton 1.
90:00 +6:08Offside, Everton. Tom Cleverley tries a through ball, but James McCarthy is caught offside.
90:00 +4:42Offside, Everton. Leighton Baines tries a through ball, but Ramiro Funes Mori is caught offside.
90:00 +3:44Attempt missed. Arouna Koné (Everton) right footed shot from the right side of the box is too high.
90:00 +2:33Delay over. They are ready to continue.
90:00 +2:30Kevin De Bruyne went off injured after Manchester City had used all subs.
89:46Delay in match Kevin De Bruyne (Manchester City) because of an injury.
88:14 BookingBooking Leighton Baines (Everton) is shown the yellow card for a bad foul.
88:02Jesús Navas (Manchester City) wins a free kick on the right wing.
88:02Foul by Leighton Baines (Everton).
86:16Attempt 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.
85:36Corner, Manchester City. Conceded by James McCarthy.
85:34Attempt blocked. Sergio Agüero (Manchester City) right footed shot from a difficult angle on the right is blocked. Assisted by Kevin De Bruyne.
84:26 BookingBooking Nicolás Otamendi (Manchester City) is shown the yellow card for a bad foul.
84:21Foul by Nicolás Otamendi (Manchester City).
84:21Arouna Koné (Everton) wins a free kick on the right wing.
83:33 BookingBooking Tom Cleverley (Everton) is shown the yellow card for a bad foul.
83:27Fernandinho (Manchester City) wins a free kick on the left wing.
83:27Foul by Tom Cleverley (Everton).
Substitution Substitution, Manchester City. Fernando replaces David Silva.
78:33David Silva (Manchester City) wins a free kick on the left wing.
78:33Foul by Gareth Barry (Everton).
77:35Raheem Sterling (Manchester City) wins a free kick in the defensive half.
77:35Foul by Seamus Coleman (Everton).
77:00 SubstitutionSubstitution Substitution, Everton. Seamus Coleman replaces John Stones.
75:58 Goal scoredGoal! 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.
75:22Corner, Manchester City. Conceded by Tom Cleverley.
75:19Attempt blocked. Fernandinho (Manchester City) right footed shot from outside the box is blocked.
75:15Attempt blocked. Kevin De Bruyne (Manchester City) right footed shot from outside the box is blocked.
74:25Fernandinho (Manchester City) wins a free kick in the attacking half.
74:25Foul by Tom Cleverley (Everton).
69:21 Goal scoredGoal! 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.
68:20Jesús Navas (Manchester City) wins a free kick in the defensive half.
68:20Foul by Tom Cleverley (Everton).
67:26Foul by Gaël Clichy (Manchester City).
67:26Arouna Koné (Everton) wins a free kick in the attacking half.
66:24Offside, Manchester City. Jesús Navas tries a through ball, but Kevin De Bruyne is caught offside.
66:03Martín Demichelis (Manchester City) wins a free kick in the defensive half.
66:03Foul by Arouna Koné (Everton).
65:28 SubstitutionSubstitution Substitution, Manchester City. Kevin De Bruyne replaces Yaya Touré.
64:22Sergio Agüero (Manchester City) wins a free kick in the attacking half.
64:22Foul by Gareth Barry (Everton).
59:20 SubstitutionSubstitution Substitution, Everton. James McCarthy replaces Leon Osman.
59:13 SubstitutionSubstitution Substitution, Everton. Arouna Koné replaces Gerard Deulofeu.
58:26Attempt missed. Nicolás Otamendi (Manchester City) header from the centre of the box misses to the left. Assisted by Jesús Navas with a cross following a corner.
58:03Corner, Manchester City. Conceded by Tom Cleverley.
58:01Attempt blocked. Raheem Sterling (Manchester City) right footed shot from the centre of the box is blocked. Assisted by Sergio Agüero.
53:37David Silva (Manchester City) hits the left post with a header from very close range. Assisted by Pablo Zabaleta with a cross.
51:12Martín Demichelis (Manchester City) wins a free kick in the defensive half.
51:12Foul by Leon Osman (Everton).
50:37Pablo Zabaleta (Manchester City) wins a free kick on the right wing.
50:37Foul by Leon Osman (Everton).
47:14Attempt saved. Gerard Deulofeu (Everton) right footed shot from the left side of the box is saved in the bottom right corner. Assisted by Ross Barkley.
46:39Corner, Manchester City. Conceded by Leighton Baines.
45:00Second Half begins Manchester City 1, Everton 1.
45:00 SubstitutionSubstitution Substitution, Manchester City. Jesús Navas replaces Fabian Delph.
45:00 +1:25 Half timeHalf Time First Half ends, Manchester City 1, Everton 1.
45:00 +1:09Nicolás Otamendi (Manchester City) wins a free kick in the defensive half.
45:00 +1:09Foul by Romelu Lukaku (Everton).
45:00 +0:41Corner, Everton. Conceded by Nicolás Otamendi.
41:07Attempt missed. Gerard Deulofeu (Everton) right footed shot from outside the box is too high from a direct free kick.
39:53Foul by Fabian Delph (Manchester City).
39:53Ross Barkley (Everton) wins a free kick in the attacking half.
38:18Corner, Manchester City. Conceded by Gareth Barry.
38:15Attempt blocked. David Silva (Manchester City) left footed shot from outside the box is blocked.
37:05Fabian Delph (Manchester City) wins a free kick in the attacking half.
37:05Foul by Tom Cleverley (Everton).
35:54Offside, Manchester City. Pablo Zabaleta tries a through ball, but Nicolás Otamendi is caught offside.
35:20Corner, Manchester City. Conceded by Joel Robles.
35:18Attempt saved. David Silva (Manchester City) left footed shot from the centre of the box is saved in the centre of the goal.
35:16Sergio Agüero (Manchester City) hits the right post with a right footed shot from outside the box. Assisted by David Silva.
34:18Nicolás Otamendi (Manchester City) wins a free kick in the defensive half.
34:18Foul by Leon Osman (Everton).
31:17Martín Demichelis (Manchester City) wins a free kick in the attacking half.
31:17Foul by Gareth Barry (Everton).
29:33Offside, Manchester City. Willy Caballero tries a through ball, but Raheem Sterling is caught offside.
27:55Yaya Touré (Manchester City) wins a free kick in the defensive half.
27:55Foul by Ross Barkley (Everton).
24:35Foul by David Silva (Manchester City).
24:35John Stones (Everton) wins a free kick in the defensive half.
23:38 Goal scoredGoal! Goal! Manchester City 1, Everton 1. Fernandinho (Manchester City) right footed shot from outside the box to the bottom left corner.
23:36Attempt blocked. Sergio Agüero (Manchester City) right footed shot from outside the box is blocked. Assisted by David Silva.
22:51Attempt missed. Yaya Touré (Manchester City) right footed shot from the right side of the box is too high. Assisted by David Silva.
19:18Attempt saved. Raheem Sterling (Manchester City) left footed shot from outside the box is saved in the bottom right corner. Assisted by David Silva.
17:20 Goal scoredGoal! Goal! Manchester City 0, Everton 1. Ross Barkley (Everton) right footed shot from outside the box to the bottom left corner. Assisted by Leon Osman.
15:20Attempt blocked. Nicolás Otamendi (Manchester City) right footed shot from outside the box is blocked. Assisted by Gaël Clichy.
14:05Corner, Manchester City. Conceded by John Stones.
10:55Foul by Raheem Sterling (Manchester City).
10:55Ramiro Funes Mori (Everton) wins a free kick in the defensive half.
10:15Attempt blocked. Raheem Sterling (Manchester City) left footed shot from the centre of the box is blocked. Assisted by Sergio Agüero.
9:49Attempt missed. Fernandinho (Manchester City) header from the centre of the box misses to the left. Assisted by David Silva with a cross following a corner.
9:28Corner, Manchester City. Conceded by Leon Osman.
4:57Offside, Manchester City. Willy Caballero tries a through ball, but Raheem Sterling is caught offside.
4:19Offside, Everton. Gareth Barry tries a through ball, but Leighton Baines is caught offside.
3:12Corner, Everton. Conceded by Nicolás Otamendi.
2:22Offside, Manchester City. Yaya Touré tries a through ball, but Raheem Sterling is caught offside.
1:55Sergio Agüero (Manchester City) wins a free kick on the left wing.
1:55Foul by Leighton Baines (Everton).
1:17Corner, Manchester City. Conceded by Ramiro Funes Mori.
0:00First Half begins.
0:00Lineups are announced and players are warming up.
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