Goals from Raheem Sterling, Phil Foden and a semi Ajayi own goal had effectively ended the contest by the break.
Gabriel Jesus added a fourth and there were further goals from Riyad Mahrez, Nicolas Otamendi and a deflected Leroy Sane shot completed the rout.
What happened?
City started in business-like fashion, looking to try and put the tie beyond Rotherham United as soon as possible with a Carabao Cup semi-final against Burton Albion to come on Wednesday.
Pep Guardiola made eight changes from the draining 2-1 win over Liverpool, with only Ederson, John Stones and Raheem Sterling remaining.
Kevin De Bruyne returned and captained the team.
In only the second minute, Gabriel Jesus saw his header clip the bar and minutes later Sterling saw his shot go narrowly wide.
Jesus again went close on eight minutes but couldn’t convert Riyad Mahrez’s inviting low cross into the six-yard box.
The Millers’ resistance, however, ended on 13 minutes when De Bruyne’s clever disguised pass picked out Sterling who glided past one defender before burying a shot past the keeper from eight yards.
Credit to the Championship strugglers, backed by more than 6,000 travelling fans, didn’t capitulate and, having survived a couple more scares, started to come into the game and ask one or two questions of the champions’ defence.
But the Blues were never less than in complete control and that dominance was underlined with a slightly fortuitous second City goal on 43 minutes.
Ilkay Gundogan had space and time on the edge of the box to spot Foden’s dart into the box and the England Under-21 star manged to control the ball with one foot only for it to hit the other knee and wrong-foot the keeper.
If that was little unlucky for Rotherham, two minutes after that, the Blues put the tie to bed as Mahrez played Kyle Walker in down the right and the England defender’s cross was turned into his own goal by Semi Ajayi.
There was little respite for the visitors who conceded a fourth seven minutes after the re-start as Sterling burst past left-back Zak Vyner before sliding the ball to Gabriel Jesus to tap home from a couple of yards out.
City continued to be ruthless and goal No.5 was perhaps the pick of the bunch as Mahrez exchanged passes with Gundogan in the box before stroking home a low drive on 73 minutes.
And the South Yorkshire side were punished again as Otamendi powered home e header from a corner, giving Gundogan his third assist on 78 minutes.
And you had to feel for Rotherham five minutes from time as sub Leroy Sane’s powerful drive clipped a Millers defender to again wrong-foot keeper Marek Rodak who was again left shaking his head.
Blues signal intentions
With 10 full internationals and an England Under-21 midfielder starting against Rotherham, City are clearly keen to keep the quest for as much silverware as possible this season.
And when there is criticism that perhaps some clubs don’t treat the competition with the respect it deserves, that accusation cannot be levelled at City.
And with a near-full Etihad Stadium this afternoon, it’s a competition that City fans clearly relish, too.
Star man: Raheem Sterling
A goal and an assist in a 56-minute cameo from the England winger.
Pep’s thoughts…
“We took it seriously and do what we have to do to be a great club.
“Have to do our job, and we did it amazingly again. There were eight or nine fresh legs and saw what their mates did on Thursday against Liverpool.
“That’s more important that we are in next round. Everyone was really, really good.”
What it means…
City go into the hat for the FA Cup fourth round with the draw to be made on the BBC tomorrow evening.
What’s next?
The home games are coming thick and fast and it’s back to the Etihad on Wednesday evening as the Blues take on Burton Albion in the Carabao Cup semi-final, first leg.
