Raheem Sterling, Phil Foden and a Semi Ajayi own goal put a strong City side into a comfortable half-time lead.
Gabriel Jesus, Riyad Mahrez, Nicolas Otamendi and Leroy Sane completed the rout as the Millers were outclassed after the break.
Some of the build-up to the game had focused on the resemblance between Guardiola and his Rotherham counterpart Paul Warne, but the similarities between the teams ended there.
The gulf in class was soon apparent as Jesus sent a header against the crossbar - the first of a hat-trick of gilt-edged chances he spurned in the first half - after just one minute.
Guardiola had made eight changes from the side which beat Liverpool on Thursday but his team was still stacked with quality and experience, with Kevin De Bruyne, fit again after injury, among those returning.
De Bruyne was at the heart of much of City’s good play as they continually picked their way through the Millers defence.
Sterling saw a chance deflected wide in the third minute and Jesus missed another as he failed to get a touch on a Mahrez cross. Mahrez then had an effort turned away by goalkeeper Marek Rodak before Sterling exchanged passes with De Bruyne and clipped home the opener after some fine footwork in the 12th minute.
Rotherham did cause City some anxious moments, notably when Anthony Forde hurried Ederson into mishitting a pass but John Stones cleared.
Jesus had another shot blocked from a De Bruyne pass before Foden doubled the lead after 43 minutes. It was hardly the cleanest of touches from the youngster as he attempted to control a cross from Ilkay Gundogan but his contact was firm enough to take the ball past Rodak.
City added another moments later as Ajayi smashed the ball into his own net attempting to cut out a Kyle Walker cross and Jesus tapped in the fourth following a blistering Sterling run after the break.
Things hardly got easier for Rotherham as City introduced Sane but Guardiola did take an opportunity to hand a debut to Dutch youngster Philippe Sandler off the bench.
Rodak had to claw off the line from team-mate Zak Vyner and he saved from Walker but Mahrez tucked home the fifth after playing a one-two with Gundogan and Otamendi headed number six from a corner.
Sane completed the scoring with a deflected shot while Ederson made a late save from Michael Smith to deny the visitors a consolation.