Manchester: Held 1-1 at Ewood Park in the initial tie, City took control of the replay at a rain-soaked Etihad Stadium thanks to a brace of goals either side of half-time from Alvaro Negredo.
Edin Dzeko added a third before Aguero scored only 50 seconds after his introduction as a 72nd-minute substitute, following a month on the sidelines with a calf injury.
Sergio Aguero. Pic/ AFP
Dzeko brought up City's 99th goal in all competitions this season to make it 5-0, leaving Blackburn's Championship counterparts Watford with plenty of food for thought ahead of their trip to the Etihad in the fourth round.
City manager Manuel Pellegrini made eight changes to the team that won 2-0 at Newcastle United on Sunday and his new-look side initially struggled to make inroads.
Dzeko snatched at a handful of early chances and a free-kick within shooting distance offered Blackburn an opportunity to strike at the other end, only for Ben Marshall to curl his shot straight at Costel Pantilimon.
Belatedly, City began to muster more of a threat, with Javi Garcia forcing Blackburn goalkeeper Paul Robinson into a sprawling save from long range and Jesus Navas bending an inviting cross across goal.
Blackburn had largely succeeded in keeping their opponents at arm's length, but with the respite of the half-time interval within touching distance, City struck.
Navas's pass found the overlapping Fernandinho and the Brazilian's whipped cross enabled Negredo to claim his 20th goal of the season with a firm downward header.
Pellegrini introduced Aleksandar Kolarov for Fernandinho at half-time and the first thing the Serbian did was create City's second goal with a superb searching pass from halfway that Negredo lifted past Robinson.
The timing of Negredo's second goal was every bit as cruel as his first, but Blackburn briefly threatened to make a game of it.
In the space of a minute, Joshua King headed over and then forced Pantilimon into a save at his near post, before Jason Lowe shot narrowly wide.
The flurry passed, however, and Dzeko made the game safe in the 67th minute when he swept a shot high into the net at the near post from Navas's low cross.
Aguero came on for Negredo and needed only two touches to make his mark, trapping a lay-off from Dzeko and swivelling before planting a low shot in the bottom-right corner with his left foot.
Dzeko added a fifth with 11 minutes remaining, finishing at the near post after the irrepressible Navas drove yet another excellent cross into the box from the right.