That it took 11 minutes for the opening goal was the only surprise here as Manchester City duly confirmed their place in the fourth round.
Having won only three of their last seven FA Cup games against sides from a lower division, Pep Guardiola was eager to guard against complacency with an unprecedented four trophies still on the agenda this season.
An experienced side and with the irrepressible Kevin De Bruyne orchestrating attacks and Raheem Sterling teasing and tormenting the overworked Rotherham defence in the hour he played, the thought of an upset was never on the cards.
It was a cruise from the moment Sterling struck his 12th goal of the campaign.
A crossfield pass from John Stones found him on the left-hand side and he exchanged passes with, inevitably, De Bruyne, and calmly finished into the corner.
The pass from De Bruyne was subtle, equally sublime, and he was imperious as always in driving his side forward.
By this point City could have been three goals clear.
Barely a minute had gone when De Bruyne - gaining much-needed match fitness following his injury absence - collected a throw from Kyle Walker on the right, burst past Ben Wiles and floated a cross for Gabriel Jesus to head against the bar.
The Brazilian was under pressure from Semi Ajayi and likewise when Riyad Mahrez drilled in a low cross that Jesus somehow missed.
It was one of those frustrating days for the frontman as he failed to make more of promising positions and, astoundingly, City had one shot of nine on target until Phil Foden claimed a fortunate second.
With two minutes to the break and the Millers offering stubborn resistance, Ilkay Gundogan ventured further forward from his midfield holding role and a chipped pass picked out the run of the teenager.
As Foden tried to control the ball, it flicked up onto his left knee and past the stranded Marek Rodak.
Rotherham’s Slovakian keeper was beaten again in added time when his clearance was cut out by Kyle Walker and the full-back linked with Mahrez and saw his inviting cross turned in by the unfortunate Semi Ajayi.
Rotherham, who had not reached the fourth round since 2014 and whose priority this season is to stay in the Championship, had succumbed and were soon swept aside as City showed the ruthless approach that had been missing in the first period.
Sterling served up Jesus for an opportunity he could not miss in the 52nd minute before Mahrez combined well with Gundogan to claim a goal of his own.
With little to do at the back, Nicolas Otamendi came up for a 78th minute corner, delivered by Gundogan and met with a powerful header that gave Rodak no chance.
There was to be no respite for Rotherham as substitute Leroy Sane made it seven from another Gundogan assist.
It was far from magnificent as City were always comfortable and sloppy at times - and that’s the scary aspect to this resounding victory.
Given their recent success in the Premier League and League Cup, it is strange to think City last won this competition in 2011.
With a strong team selection here demonstrating his intent, even with a League Cup semi-final meeting with Burton to follow on Wednesday, Guardiola, no doubt, would love to enjoy his first FA Cup triumph.
Teams
Manchester City: Ederson; Walker, Stones (Danilo 75), Otamendi, Zinchenko; Foden, Gundogan, De Bruyne (Sandler 67); Mahrez, Jesus, Sterling (Sane 57)
Subs not used: Muric, Laporte, Fernandinho, B Silva
Rotherham United: Rodak; Vyner (Wood 89), Ajayi, Robertson, Mattock; Taylor (Raggett 74), Wiles, Forde, Vaulks, Williams (Palmer 90); Smith
Subs not used: Price, Newell, Jones
