City started brightly and were ahead after 14 minutes when Kevin De Bruyne, returning to the starting lineup for the first time since early November, skipped past Hamza Choudhury and planted a fine finish past Danny Ward at the near post from 20 yards.
It was a brilliant moment of individual quality; a reminder of what City have been missing in his absence.
Leicester, who came into the match yet to concede a goal in this season’s Carabao Cup, were visibly dejected, and it was City who were dominating the ball. Riyad Mahrez blasted one over the bar from close range after Brahim Diaz's effort was blocked and the Algerian will feel he should have at least made the 'keeper work.
Early in the second half, Sergio Aguero, back after a groin problem, was put clean through by Mahrez, but the Argentine's effort was well saved Ward, and Mahrez went close soon after when his curling left-footed effort from the edge of the area flashed just over the bar.
But Leicester, who had been outplayed for much of the game, weren't finished just yet, and with 73 minutes on the clock Wilfred Ndidi played a fine ball over the top that took City’s defence out of the game, and Mark Albrighton equalised with an emphatic finish past Muric.
Mahrez had another good chance moments later, but his effort went just wide, before substitute Gabriel Jesus had a penalty claim turned down after he was brought down by Choudhury and Phil Foden spurned a chance when clean through after Ilkay Gundogan's clever slide-rule pass.
Penalties would determine which of these sides would make it through to the semi-finals - and it was City who once again emerged victorious.
Christian Fuchs was the first to miss, before Muric saved from James Maddison and Caglar Soyunchu. Zinchenko's fine top-corner effort made it 3-1 to the Blues in the shoot-out to seal the win and keep us on course for our fourth EFL Cup triumph in six seasons.
Man of the match: Kevin De Bruyne
It was 70 minutes of pure class from the returning Belgian, who deserves huge praise for his performance.
Special mention for Eric Garcia, too, who delivered a composed display. For a 17-year-old to look so calm and comfortable on the ball was quite something.
Our results during De Bruyne’s injury layoff were exceptional, but we’ve doubtless missed his excellence. He’s tenacious in the tackle, never shirks defensive work and plays with the kind of diligence Guardiola demands.
But, obviously, it’s his quality in possession which so often excites. Passing, shooting, the ability to beat a defender…he's the most well-rounded midfielder in English football.
And perhaps the rest he has had whilst sidelined will prove to be a good thing in the long run. He had a demanding 2017-18, playing 63 times for club and country, a gruelling schedule that probably cannot be maintained. Time will tell if he looks fresher when others are beginning to flag.
He’s back with a bang and City will be better for it in the coming weeks.
Pep's philosphy deeply ingrained
Eight changes from the win over Everton, a debut for 17-year-old Garcia and a starting lineup with an average age of 23, yet the quality remains high.
Pep Guardiola’s ideas are a so deep-rooted, it doesn’t seem to matter which players are selected, the vibrancy of our play remains the same and our principles never waver.
Slick passing, plenty of movement, players given freedom to express themselves and a permanent desire to attack. This is our blueprint, regardless of personnel.
Reaction: Pep Guardiola
“We played with Kevin and Sergio who cannot play the full 90 minutes We played with a guy who is 17 years old and Aro who is 20.
“We made quite a god performance. Of course, we had chances to win the game before.
“It was the same last season when we won with penalties thanks to Claudio. This year it was Aro.
"Raheem took that decision [to chip his penalty], unfortunately he missed it but that is OK."
It’s back to Premier League duties this weekend when City host Crystal Palace on Saturday, before a quick return to the King Power Stadium on Boxing Day.