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.
City boss Pep Guardiola was delighted with Kevin de Bruyne's performance on the day.
“We spoke with him yesterday to play 65/70 minutes for his rhythm and his injury," said Guardiola.
“He played incredible, created a good amount of chances and has a vision that others aren't able to see.
“Last season he played incredible minutes but hopefully in the second leg of the season he will help us because we need him.
“I said many times. Without him last season maybe it wouldn't have been possible.
“We try to be a team and so far we have done incredible with results.
“We have to carry on, now he is back and he is now fresh in mind and legs. Today he was our captain and he showed why."