Sadio Mane's red card proved the decisive moment as he was dismissed for a reckless challenge on goalkeeper Ederson.
The visitors had started the brighter but found themselves behind as Sergio Aguero rounded Simon Mignolet and slotted in.
Gabriel Jesus added a second shortly after Mane's red before Aguero teed his strike partner up for another.
Substitute Leroy Sane scored twice late on as
City made the most of the man advantage.
1. Mane red the turning point
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