Everton extended their 2-1 advantage from the first leg when Ross Barkley scored a fine individual goal in the 18th minute, but Fernandinho quickly equalised before substitute De Bruyne levelled the tie and then set up Sergio Aguero to complete a 4-3 aggregate victory in the 76th minute.
Replays, however, suggested that Raheem Sterling had taken the ball beyond the byline before cutting it back for De Bruyne to score and the former Wolfsburg winger finished the match on a stretcher after his knee buckled in a late challenge with Ramiro Funes Mori.
City's win deprived Everton of a meeting with Liverpool -- who overcame Stoke City on penalties on Tuesday -- in what would have been the first all-Merseyside major final since the 1988-89 FA Cup and the first League Cup final to feature the Goodison Park club since 1984.
With David Silva orchestrating the hosts' attacks, City looked to dictate the game, but Everton posed a threat on the break and after menacing incursions by Gerard Deulofeu and Barkley, the England playmaker extended the visitors' aggregate lead.
It was a goal that demonstrated both the brilliance of Barkley and City's defensive porousness as the Everton number 20 evaded the sliding Nicolas Otamendi and foxed Fabian Delph with a stylish feint before steering a low shot into City goalkeeper Willy Caballero's bottom-right corner.
Barkley's strike left City needing two goals to stay in the tie, but after Sterling had tested Joel Robles and Yaya Toure had curled over, they halved the aggregate deficit.
After Aguero's shot was blocked by returning Everton skipper Phil Jagielka, Fernandinho followed in with a right-foot drive that clipped Leighton Baines's heel and left Robles clutching at thin air.
City almost levelled the tie nine minutes before the interval, Aguero thumping a shot against the right-hand upright from outside the box and Sterling seeing his follow-up swatted behind by Robles.
- Fury -
Barkley created a chance for Deulofeu early in the second half, the Spaniard drawing a save from Caballero with a side-foot shot, but with Jesus Navas on in place of Delph, City had a new outlet on the right flank and they began to bang on the door.
Aguero miscued, uncharacteristically, from a Navas cross, Silva headed a Pablo Zabaleta cross against the post and Tom Cleverley had to produce a sliding block to thwart Sterling.
Everton manager Roberto Martinez added fresh legs in the form of James McCarthy and Arouna Kone.
City boss Manuel Pellegrini responded by replacing Toure with De Bruyne, City's record £55 million ($78.3 million, 71.9 million euros) signing, and four minutes after coming on the Belgian levelled the tie.
Sterling had moved to the left following Navas's entrance and he showed England colleague John Stones a clean pair of heels before pulling the ball back for De Bruyne, who side-footed home.
To the fury of Evertonians on social media, replays showed that the ball had just crossed the line before Sterling played it into the box.
The mood of those in royal blue plummeted six minutes later when De Bruyne shaped a cross into the box from the right and Aguero glanced a deft header past Robles to send City to Wembley.
De Bruyne had made a stunning impact, but his night ended prematurely when he went down on the corner of the Everton box and had to be carried off on a stretcher.