Pep Guardiola's League Cup holders were two up by half-time at the Etihad Stadium thanks to goals from Nicolas Otamendi and Aguero.
Guardiola had made nine changes to the team that beat Aston Villa in the Premier League on Saturday, giving a debut to 18-year-old midfielder Tommy Doyle.
Doyle's grandfather Mike was City's captain when they won the League Cup in 1976 and the club remain on course to win the tournament for a seventh time.
City, who have lifted the trophy three times in the last four seasons, began the fourth round tie serenaded by chants of "We want 10" in reference to Southampton's 9-0 thrashing by Leicester on Friday.