Mohamed Salah had given the Reds the lead at Etihad Stadium after 17 minutes with a fine first-time finish, before Julian Alvarez netted an equaliser 10 minutes later.
But second-half goals from Kevin De Bruyne, Ilkay Gundogan and Jack Grealish then clinched the three points for the hosts.
Team news
Jordan Henderson and Harvey Elliott were the two changes introduced to Liverpool's line-up following the international break.
Alisson, Alexander-Arnold, Konate, Van Dijk, Robertson (Tsimikas, 70), Fabinho, Henderson, Elliott (Oxlade-Chamberlain, 70), Jota (Firmino, 70), Salah (Nunez, 70), Gakpo (Milner, 82).
Unused substitutes: Kelleher, Gomez, Arthur, Matip.
First half
The visitors absorbed some early City pressure but looked threatening whenever presented with the opportunity to venture forward.
Alisson Becker was forced to make a pair of saves, first denying Gundogan and then a powerful effort from Rodri, before the Reds went up the other end to open the scoring.
Diogo Jota successfully evaded the offside trap to latch on to Trent Alexander-Arnold's clip over the top. Jota ran through on goal but was held up by Manuel Akanji, though he did manage to lay the ball off.
That presented Salah with a sighting of Ederson's goal and the Egyptian went on to curl a beautiful effort into the far corner first time.
City threatened twice with a quick response but Gundogan and Riyad Mahrez were off target when in good positions inside the area.
Liverpool's lead was nearly doubled when Salah led a rapid breakaway, only for Grealish to track back and cut out the opening goalscorer's intended square for Jota.
Grealish had saved a goal and then created one moments later. Interplay between Mahrez and Gundogan saw the ball worked out to the left wing, where Grealish crossed for Alvarez to convert from close range.
Second half
The Reds went behind in the contest fewer than 60 seconds after the restart.
Alvarez played a pass that sent Mahrez free on the right channel, with a cross then sent into the penalty area that allowed De Bruyne a simple finish.
And in minute 53 City then secured a two-goal advantage when Gundogan was in position to convert from inside the area, after an initial shot from Alvarez had been blocked.
Cody Gakpo nearly pulled one back for Liverpool but watched his shot towards goal get deflected for a corner.
Alisson was then at full stretch on the hour mark to tip behind a hit from Grealish, but could do nothing to keep out another effort from the City attacker 14 minutes later.
Playing a one-two with De Bruyne, Grealish met a cutback inside the box and slid a finish beyond the Brazilian goalkeeper to complete the scoring in the game.