After Aleksandar Kolarov's early free kick opened the scoring, the Bosnian striker took the game away from their Championship opponents to reach the Capital One Cup semi-finals
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 Capital One Cup appearances and City's 19th in six matches across all competitions.
The Foxes - 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.
|By Tom Doyle
Leicester City got a good reception from their supporters for a much-improved second-half display against Manchester City but, in the end, the quality of Manuel Pellegrini's squad shone through.
It speaks volumes that the Chilean was able to make eight changes and still see his side progress to the semi-finals of the Capital One Cup, with a stunning free kick from Aleksandar Kolarov and a poacher's effort from Edin Dzeko setting the visitors on their way.
The Foxes were lifeless in the first 45 minutes and many inside the stadium would have feared a drubbing when Dzeko added a third but Nigel Pearson's side improved, with Lloyd Dyer's late effort even sparking a potential fightback for the Championship side.
David Silva and James Milner were the chief architects of Leicester's destruction, though Pellegrini will rue the hamstring injury to Pablo Zabaleta, with the influential right-back an unwanted casualty on an otherwise fine night for City.
The visitors' lineup 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 - who sit 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 Pellegrini's men almost caught their opponents cold on the counterattack.
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, though, 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 the forward doubled his tally following 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.