Mane was shown a straight red card in the first half for a high challenge on Ederson that led to the City goalkeeper being carried off on a stretcher.
City were already leading at that point through Sergio Aguero but Gabriel Jesus and substitute Leroy Sane then both struck twice in a commanding performance.
City later reported that Ederson was not concussed and was checked for facial fractures at the medical institute adjacent to their training complex before returning to the stadium.
The hosts' performance represented a notable lifting of the tempo after a solid opening to the campaign while Liverpool's impressive start was brought to a sudden halt.
City were without defensive linchpin Vincent Kompany and, worried by Liverpool's formidable forward line, set up cautiously with wing-backs playing deep and midfielder Fernandinho just in front of the back five.
It did not prevent them looking jittery, with Nicolas Otamendi enduring a particularly difficult start up against the pace of Mohamed Salah.
City were a different proposition coming forward and Fernandinho tested Simon Mignolet from distance before Kevin De Bruyne split the Liverpool defence open with a superb through-ball for Aguero's 25th-minute opener.
Aguero made no mistake as he rounded Mignolet and tucked home his sixth goal in as many Premier League home appearances against the Reds.
Liverpool responded with Mane racing clear only to be felled on the edge of the area by Fernandinho. Emre Can blasted the resulting free-kick wide before Salah failed to beat Ederson from close range.
The game's major talking point came after 37 minutes as Mane chased a long ball over the top and raised his boot as Ederson came rushing out. He accidentally caught the Brazilian in the head and the keeper instantly fell to the ground.