An emphatic win, City's 10th in a row in the league and first at Anfield since 2003, moved Pep Guardiola's side to 50 points from 22 games, five more than second-placed Manchester United who have played a game more.
Champions Liverpool are now 10 points behind City in fourth spot and if any more evidence were needed that they have gone off the rails it was the sight of Alisson, a rock for the past two seasons, effectively gifting City the points.