The Argentina striker set City on its way in the 15th minute with a stunning individual effort and although he later missed a second-half penalty, the hosts had too much for Leicester as they set up a match at Notts County in the fourth round.
Patrick Vieira and Adam Johnson scored in the space of 77 seconds to put Roberto Mancini's side 3-1 up at the break and Aleksandar Kolarov's late finish saw off the plucky visitors, coached by former City manager Sven-Goran Eriksson.
Premier League struggler Wolverhampton thrashed Doncaster 5-0 to progress and will next play Stoke, which beat Cardiff 2-0 thanks to two extra-time goals by striker Jon Walters.
Arsenal travels to Leeds, which plays in the second-tier League Championship, on Wednesday in the other third-round replay.
