Two goals each from Gabriel Jesus and Leroy Sane after Sadio Mane was shown a red card added to Sergio Aguero's first-half opener to earn the win for Pep Guardiola's side.
Mane was sent off in controversial circumstances after a collision with Ederson. The Senegal international's foot caught the face of the Brazilian goalkeeper, who was subsequently stretchered off.
As Mane appeared to be looking at the ball and unaware of Ederson, the decision sparked immediate debate among former players and fans.
City, however, capitalised on their numerical advantage and recorded a scoreline over the Merseyside club that few in the stadium will have ever seen before.
Not since March 1937, when they beat them 5-1, have City scored five or more goals in a game versus Liverpool.
Meanwhile, Aguero became the highest-scoring non-European player in Premier League history with his 124th strike, overtaking Dwight Yorke.
He has now scored in all six of his Premier League appearances against the Reds at the Etihad Stadium, netting once in each game and making him the fourth player in the league's history to score in six consecutive home games against a single side.
While City and Aguero take only positives, it was a dark day for Jurgen Klopp, matching the worst defeat in his career since his days at Mainz.