After holding out for much of the first half, Gary Bowyer's men were put to the sword in the second period as Alvaro Negredo and Edin Dzeko hit doubles in a thumping replay win
Rovers had forced a replay after an impressive display at Ewood Park and Manuel Pellegrini's men continued to struggle to break down their stubborn opponents until Alvaro Negredo powered home a header in first-half stoppage time.
That would open the floodgates, with the home side doubling their lead moments after the restart as Negredo dinked the ball over substitute keeper Simon Eastwood after a wonderful pass from Aleksandar Kolarov, before Edin Dzeko got in on the act with a thumping finish.
City had another reason to cheer when Aguero made his long-awaited return from injury, and he took barely 50 seconds to score, swivelling in the box with his first touch before burying the ball with his second to notch his 20th goal of the season.
Dzeko rounded off the scoring with his second goal of the night, once again combining with Navas before stroking the ball beyond Eastwood, taking City's goal tally for the season to 99.
City made eight changes from the side that beat Newcastle United 2-0 in the Premier League on Sunday, Negredo, Fernandinho and Dzeko the only players retained, while striker Jordan Rhodes and defender Scott Dann both missed out through injury for Blackburn.
The hosts made the better start to proceedings, Dzeko twice going close to opening the scoring in the first 10 minutes, but Rovers soon managed to gain a foothold in the game and provided frustrating opposition for City, who were largely reduced to long-range efforts in the first half.
However, the hosts would have taken the lead had Negredo or Fernandinho been able to make contact with Navas' low delivery across the face of goal which narrowly evaded a sky blue shirt.
Pellegrini's men finally broke the deadlock just before the interval as Negredo headed home Fernandinho's right-wing cross with a powerful close-range header, a goal which would crush Blackburn's spirited resistance.
Both teams made changes during the interval, Kolarov replacing Fernandinho for City and injured Blackburn goalkeeper Paul Robinson making way for Eastwood.
And Negredo all but ensured City's place in the fourth round within two minutes of the restart, the Spaniard latching on to an excellent pass from Kolarov to lift the ball over Eastwood and net his 16th goal in 12 games at the Etihad Stadium this term.
City took their foot off the gas following that goal and Blackburn could have cut the deficit had substitute Joshua King taken either of two golden opportunities midway through the second half.
Blackburn were made to pay for King's profligacy in the 67th minute, though, as Dzeko lashed home a Navas pull back to further underline City's dominance.
Aguero replaced Negredo five minutes later and made an instant impact as the Argentina striker turned home a lay-off from Dzeko to mark his return from injury in style.
Bosnia international Dzeko concluded the scoring with another superb finish, rifling Navas' low cross past Eastwood at his near post, as City continued their stunning home form to set up a fourth-round tie with Watford.