A second half salvo from City saw Rovers succumb at the Etihad Stadium.
After a first half in which Rovers were more than a match for their expensively assembled hosts, a goal right on 45 gave City the edge that they would never relinquish.
Roared on by some 4500 Rovers fans, the visitors gave their all, but Alvaro Negredo's strike on the stroke of half time put City in front.
Negredo bagged a second almost immediately after the resumption and from then on there was only going to be one winner.
Edin Dzeko bagged a brace either side of a Sergio Aguero strike a minute after his introduction, as City picked of Rovers on the break.
The Lancastrians never gave up, 16-year-old Connor Mahoney was even given his debut, but as the supporters sang loud and proud Rovers couldn't reward their efforts with a goal themselves.
The cup campaign is over, all attention now shifts to this Saturday's key match against Nottingham Forest.
For the cup replay Gary Bowyer made three changes from the side that defeated Doncaster Rovers at the weekend.
Two of the changes were enforced as Scott Dann (groin) and Jordan Rhodes (foot) both missed out through injury. The third change saw Rudy Gestede, who limped out of Saturday's match with cramp, drop to the bench.
The three coming into the side were Matt Kilgallon to partner captain Grant Hanley in defence, Chris Taylor and DJ Campbell.
Typical Manchester rain greeted the two sides as they took to the field, Rovers' roared on by some 4500 following faithful.
It was an even opening period, Dzeko over with an early header, whilst Campbell just couldn't reach a pass from Marshall in the opposing box.
As play settled down it was City with the majority of possession, Rovers content to hold their shape and pick their opportunities when given. A Fernandinho ball over the top saw Negredo feed Dzeko once more but the Bosnian was again off target.
From a Tom Cairney corner Ben Marshall fired wide, then after Cairney had seen a fine run halted illegally, Marshall curled the resulting free-kick into the arms of Costel Pantilimon. The Romanian showing better handling than in the initial round at Ewood.
At the other end Paul Robinson got down to claim a Javi Garcia long-range effort, before a Jesus Navis cross from the right saw hearts in the mouths of the Rovers contingent, but Negredo and Fernandinho both failed to connect as they slid into the six-yard box.
Good work by DJ Campbell lead to Chris Taylor shooting wide, whilst a cross from James Milner just evaded Micah Richards at the back post.
In a near carbon copy of the first game, just as the fourth official had indicated a minute of added time to play City caught Rovers on the break, Fernandinho stole away down the right and centred to where Alvaro Negredo headed home.
It was harsh on Rovers as they had worked tirelessly in the first half, the added minute by the officials questionable.
The break saw Rovers forced into a change as Paul Robinson was replaced by Simon Eastwood at the resumption of the second half.
And although Eastwood got an early touch of the ball he was soon picking it out of his own net.
Aleksandar Kolarov, himself a half-time substitute, sent over a ball from half way, Grant Hanley missed with his clearance and Negredo needed no second invitation to add his second of the game. His 21st of the season.
It wasn't the start to the second half that was asked of Rovers.
Boosted by the early goal City went in search for more as the lively Kolarov twice fired over, but to their credit Rovers didn't let their heads drop.
Josh King was introduced on the hour mark and within four minutes he almost pulled a goal back for Rovers.
Keeping possession well, Rovers worked the ball over to the left to where Ben Marshall cut in to centre, King rose well on the six-yard line but couldn't keep his header down.
A minute later and the Norwegian international was in the thick of the action once more, racing clear of Nastasic to get to Cairney's through ball, but Pantilimon saved his shot well.
Then it was Jason Lowe's turn to go close, his effort from outside the area striking Joleon Lescott, the ball flashing just wide.
Just as it looked like Rovers were building up a head of steam City struck a decisive third.
There seemed little on as Jesus Navas crossed for Edin Dzeko but a swift turn and shot saw him lash a stupendous shot into the roof of the net.
Rovers were briefly knocked out of their stride but came once more, Marshall, twisting and turning, crossed for Jason Lowe, but he chose to look for King rather than head goalwards himself and Nastasic cleared. From the resulting Marshall corner, Matt Kilgallon saw his downward header cleared off the line by Micah Richards.
Sergio Aguero replaced two-goal hero Alvaro Negredo on 72 minutes and within seconds the Argentinian was on the scoresheet.
Gael Clichy did well down the left to get his cross to the near post to where Dzeko turned and crossed for Aguero and he fired through a host of bodies and beyond Eastwood.
After an extended spell of Rovers possession Jesus Navas and Edin Dzeko combined for City's fifth on the night, Navas crossing for Dzeko to score from an impossible angle at the near post.
The Rovers fans, who outsung their opponents throughout, responded by doing the Poznan, despite the scoreline the 4500 Roverites throughly enjoined themselves.
There was still time for Rovers to give 16-year-old Connor Mahoney, the former Accrington man impressing in a four minute cameo.
The Rovers fans sang loud throughout, it was just a pity they weren't rewarded with at least one goal on the night.
The players and backroom staff all headed over to the 4500 Rovers fans at the end of the game, their efforts did not go un-noticed.
MAN CITY: Pantilimon, Richards (sub Huws 77 mins), Lescott, Milner (c), Negredo (sub Aguero 72 mins), Dzeko, Garcia, Navas, Clichy, Fernandinho (sub Kolarov 46 mins), Nastasic.
Subs not used: Hart (GK), Zabaleta, Demichelis, Lopes.
Goals: Negredo 45+1, 46 mins, Dzeko 67, 79 mins, Aguero 73 mins.
Booked: Milner, Kolarov.
ROVERS: Robinson (sub Eastwood 46 mins), Henley, Hanley (c), Kilgallon, Lowe, Williamson (sub Mahoney 89 mins), Cairney, Taylor, Marshall, Campbell (sub King 59 mins).
Subs not used: Dunn, Olsson, Rochina, Gestede.
Attendance: 33,102 including 4,369 Rovers fans.