Match ends, Everton 2(2), Leicester City 2(4).
Leicester City survived a second-half Everton comeback to win 4-2 on penalties after a 2-2 draw and set up a Carabao Cup semi-final with Aston Villa.
The Foxes had raced ahead with two goals in three first-half minutes from James Maddison and Jonny Evans.
But Tom Davies got Everton back into it with a volley before Leighton Baines' strike meant a shootout was needed.
Kasper Schmeichel made two saves before Jamie Vardy converted the decisive penalty to send Leicester through.
Victory means the Foxes have reached the League Cup semi-finals for the first time since the 1999-2000 campaign, when they went on to win the trophy.
Leicester will host Aston Villa in the first leg of the semi-final in the week commencing 6 January.
Foxes on hunt for silverware
It was a dramatic end to a game that Leicester had looked unlikely to lose for an hour, with the Foxes comfortable at 2-0 up.
The win will have come as a relief for boss Brendan Rodgers, whose team selection suggested he sees this competition as a realistic route to a trophy, despite his side sitting second in the Premier League.
Rodgers made just three changes for the game, despite upcoming league fixtures against Manchester City and leaders Liverpool, and the Foxes came flying out of the traps as they attacked with pace and precision.
Everton's two second-half goals would, on the face of it, suggest a worrying capitulation, particularly after Leicester were held by Norwich at the weekend.
But in truth, they should have been out of sight long before Everton got back into the game, with Ayoze Perez seeing a powerful long-range strike tipped over by Jordan Pickford before the Toffees keeper denied Dennis Praet with his feet.
In the end they got the job done with the reliable Vardy coolly despatching his penalty to put Leicester into the last four.
Ferguson handing Everton over in good shape?
It appears increasingly likely that Carlo Ancelotti will be the next Everton boss, with reports on Wednesday strongly suggesting the Italian has agreed a deal to take charge of the club.
Caretaker boss Duncan Ferguson has certainly done an admirable job of clearing the doom and gloom around the club after they slipped perilously close to the relegation zone under previous incumbent Marco Silva.
The Toffees legend has overseen a win against Chelsea and a credible draw at Manchester United, and against Leicester the improved work rate was once again evident.
Even after going two goals down they did not give up and when Davies volleyed home in the second half the 39,000-strong crowd roared the home side on to grab an equaliser.
Ultimately they fell just short of victory but Everton's players showed a fight and desire that has been missing for large parts of the season and that alone will have sent many Toffees fans home happy.
'He really studies penalty takers' - what they said
Leicester City manager Brendan Rodgers speaking to BBC Leicester: "He's [Kasper Schmeichel] got an intuition of where the ball is going to go, he does his work, really studies penalty takers. His anticipation is absolutely brilliant and his speed and agility in the goal is absolutely fantastic.
"When you get to the semi-finals against any team, it's going to be a tough game. But we just have to focus on the games up until that point and make sure that you're going in with good rhythm and good form."
Man of the match - Kasper Schmeichel (Leicester)
Twenty nine not out for Rodgers - the stats
- Leicester manager Brendan Rodgers has won his last 29 domestic cup ties in charge of Liverpool, Celtic and the Foxes.
- Everton's Leighton Baines scored his first goal for the Toffees since November 2017 against Crystal Palace, 760 days ago.
- Leicester's James Maddison has been directly involved in nine goals in his last eight appearances in the EFL Cup (four goals, five assists), scoring in all three games this season.
- Leicester's second goal scored by Jonny Evans was their 50th in all competitions this season, becoming the sixth Premier League team to reach that tally (also Manchester City, Liverpool, Chelsea, Spurs and Wolves).
- Jamie Vardy has been directly involved in 30 goals in his 29 appearances under Rodgers in all competitions for Leicester (25 goals, 5 assists).
Everton host Arsenal in the Premier League on Saturday, 21 December (12:30 GMT) while Leicester travel to Manchester City later on the same day (17:30).
- 17IwobiSubstituted forTosunat 78'minutes
- 20BernardSubstituted forKeanat 45'minutes
- 7RicharlisonSubstituted forGordonat 84'minutes
- 21Ricardo Pereira
- 17PérezSubstituted forGrayat 69'minutes
- 26PraetSubstituted forChoudhuryat 86'minutes
- 11AlbrightonSubstituted forSöyüncüat 82'minutes
- Jonathan Moss
- Shots on Target
Penalty Shootout ends, Everton 2(2), Leicester City 2(4).
Goal! Everton 2(2), Leicester City 2(4). Jamie Vardy (Leicester City) converts the penalty with a right footed shot to the bottom right corner.
Goal! Everton 2(2), Leicester City 2(3). Dominic Calvert-Lewin (Everton) converts the penalty with a right footed shot to the bottom left corner.
Goal! Everton 2(1), Leicester City 2(3). Demarai Gray (Leicester City) converts the penalty with a right footed shot to the bottom right corner.
Goal! Everton 2(1), Leicester City 2(2). Mason Holgate (Everton) converts the penalty with a right footed shot to the high centre of the goal.
Goal! Everton 2, Leicester City 2(2). Ricardo Pereira (Leicester City) converts the penalty with a right footed shot to the bottom left corner.
Penalty saved! Leighton Baines (Everton) fails to capitalise on this great opportunity, left footed shot saved in the bottom left corner.
Goal! Everton 2, Leicester City 2(1). Ben Chilwell (Leicester City) converts the penalty with a left footed shot to the bottom right corner.
Penalty saved! Cenk Tosun (Everton) fails to capitalise on this great opportunity, right footed shot saved in the bottom left corner.
Penalty saved! James Maddison (Leicester City) fails to capitalise on this great opportunity, right footed shot saved in the bottom left corner.
Penalty Shootout begins Everton 2, Leicester City 2.
Second Half ends, Everton 2, Leicester City 2.
Corner, Everton. Conceded by Çaglar Söyüncü.
Attempt saved. Jamie Vardy (Leicester City) left footed shot from outside the box is saved in the bottom left corner. Assisted by Çaglar Söyüncü.
James Maddison (Leicester City) wins a free kick on the left wing.
Foul by Séamus Coleman (Everton).
Goal! Everton 2, Leicester City 2. Leighton Baines (Everton) left footed shot from outside the box to the top left corner. Assisted by Cenk Tosun.
Attempt missed. James Maddison (Leicester City) right footed shot from outside the box is close, but misses the top right corner. Assisted by Hamza Choudhury.
Corner, Everton. Conceded by James Maddison.