Aleksandar Kolarov opened the scoring early in the first half with a stunning 30-yard free kick, and Edin Dzeko doubled the visitors’ lead just before the break with a close-range header.
The Bosnian striker piled more misery on Leicester eight minutes into the second half with his seventh goal in eight League Cup appearances and Manchester City’s 19th in six matches.
Leicester - the last Championship representatives in the competition - struggled to stretch Joe Hart but were able to grab a late consolation as Lloyd Dyer netted his seventh goal of the season.
Manuel Pellegrini’s men will have their sights set on a first League Cup crown since 1976, having reached a third semi-final in five seasons.
Manchester City's line-up showed eight changes from the comprehensive 6-3 victory over Premier League leaders Arsenal, with only Pablo Zabaleta, Vincent Kompany and David Silva keeping their places.
Gary Taylor-Fletcher made only his second start for Leicester - third in the Championship - as one of four alterations to the team who drew with Burnley.
The visitors made a quick start at the King Power Stadium and, after coming close to opening the scoring in the sixth minute, moved ahead in the eighth.
Dzeko was fouled by Anthony Knockaert, and Kolarov curled the resulting free-kick up and over the wall into the top-left corner.
Leicester worked their way back into the game with a high pressing game but chances were at a premium, and Manchester City almost caught their opponents cold on the counter-attack.
David Silva released Kolarov down the left and he rolled the ball into the unmarked Dzeko, but goalkeeper Kasper Schmeichel spread himself brilliantly to deny the Bosnian and Jack Rodwell was unable to convert the rebound.
With four minutes of the half remaining the Premier League side did double their lead through Dzeko.
James Milner was released on the left and delivered a perfectly chipped pass for his team-mate, who nonchalantly headed beyond Schmeichel.
The visitors picked up where they left off in the second half as Dzeko doubled his tally after more good work from Milner.
After the England international had evaded challenges on the left, he found Dzeko unmarked in the penalty area and the 27-year-old fired home first time from 14 yards.
As Manchester City took their foot off the gas the hosts grabbed a 77th-minute consolation, Dyer's effort deflecting off Vincent Kompany to leave Hart wrong-footed.
