Reeling from their its 9-0 Premier League trouncing at the hands of Leicester City last weekend, Southampton, in the first of two outings against City in the space of four days, was little match for Pep Guardiola's side.
Nicolas Otamendi and Aguero had City comfortably in control by half-time, with the latter on hand to nudge City further ahead 11 minutes after the restart.
Two stops in quick succession from Claudio Bravo looked to have ended Southampton's hopes of a consolation, but Jack Stephens headed in with 15 minutes remaining to ensure Ralph Hasenhuttl's side restored some pride.
Southampton went behind after 10 minutes against Leicester, but it did manage to hold on for slightly longer in this one.
However, having already kept Angelino at bay, Alex McCarthy could do little to deny Otamendi the opener in the 20th minute, City's centre-back rising between Jan Bednarek and Oriol Romeu to head home.
Aguero should have done better to get a close-range free-kick on target shortly after the half-hour, but he made no mistake when he tucked in from Kyle Walker's cross at the culmination of a slick team move.
City soon had its third early in the second half, Aguero reacting sharply to turn in Riyad Mahrez's deflected shot moments after McCarthy had kept out Bernardo Silva's prod.
Bednarek made an outstanding block from Mahrez's close-range effort, before Bravo was finally called into action to keep out a Sofiane Boufal strike.
While the former Barcelona goalkeeper could not deny Stephens to preserve his clean sheet, City still comfortably claimed a first win over its opponents in the competition.