Gabriel Jesus struck twice while Sergio Aguero and Leroy Sane netted a brace as the home side ended up running riot against 10-men.
But the game had been in the balance – with City leading by a single goal – when Jon Moss sent off the Senegal forward.
Both sides had early chances with Fernandinho bringing a smart save out of Simon Mignolet with a low drive.
And Roberto Firmino failed to get a proper connection on Mo Salah’s cross, allowing Ederson to save easily.
But the breakthrough came when Kevin de Bruyne‘s lovely through ball sent Sergio Aguero racing clear and he rounded Mignolet and finished easily.
The Kop could have hit back when Mane played in Salah but Ederson did superbly to save.
The big moment came on 36 minutes when Ederson came charging out of his goal and headed clear.
Mane – arriving a split second later connecting with the side of the Brazilian’s head with his high boot – and Jon Moss showed a straight red.
Ederson needed nine minutes of treatment on a suspected fractured cheekbone and headed straight off to a nearby medical centre.
He was replaced by Claudio Bravo, making his first appearance of the season after a nightmare first year at the Etihad.
But City were determined to make the most of their extra man and doubled their lead in first half stoppage time.
De Bruyne was again the provider as his cross was emphatically headed beyond Mignolet – a sweet moment as he had seen a header chalked off a couple of minutes earlier.
Jurgen Klopp threw on Alex Oxlade Chamberlain for his debut at the break to stiffen up the middle of the park.