A double from Edin Dzeko helped Manuel Pellegrini's side move past the final eight and into the last four as their progress under the guidance of the Chilean continues.
Aleksandar Kolarov kicked things off with a stunning free-kick from 30 yards in the eighth minute before Dzeko added a second when he headed home James Milner's floated cross four minutes before the break.
City were in cruise control when Dzeko grabbed his second in the 53rd minute, again being fed by Milner, to slot home from about 12 yards.
Lloyd Dyer pulled one back for the Foxes with just over ten minutes left but the damage had been done as City move through to the semis which take place on the week commencing January 6, 2014.
Capital One Cup - quarter-final
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