City took the lead through Gabriel Jesus in the 17th minute and Raheem Sterling doubled the advantage two minutes later with a tap-in that capped a flowing move.
David Silva got City's third with a simple finish after another incisive raid in the 27th minute.
Stoke's Mame Biram Diouf reduced the deficit with a deflected effort in the 44th minute and City's defence was breached for just the fourth time in the league this season when Kyle Walker scored an own goal two minutes after the interval.
But Jesus's second goal in the 55th minute restored order and his compatriot Fernandinho put the result beyond doubt five minutes later.
City reached six goals in a game for the second time this season as Leroy Sane netted in the 62nd minute.
Bernando Silva's first City strike, in the 78th minute, made it 24 goals in his team's last five league games.
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