Fabinho rifled the Reds into a sixth-minute lead moments after the visitor was left seething when Trent Alexander-Arnold was not punished for a seeming handball in the penalty area.
Mohamed Salah doubled the lead in a pulsating start and Sadio Mane completed the ransacking early in the second half as Liverpool's hopes of ending 30 years of title pain earned a monumental boost despite Bernardo Silva's 78th-minute strike giving the visitor late hope of a revival.
Liverpool – unbeaten in 17 Premier League contests with City at Anfield – has an eight-point lead over Chelsea and Leicester City but perhaps far more significant for Jurgen Klopp's men, is the cushion of nine they have over Pep Guardiola's defending champion.
City was outraged not to be awarded a fifth-minute penalty for handball against Alexander-Arnold and its sense of injustice was exacerbated less 60 seconds later when Fabinho picked up Ilkay Gundogan's poor clearance and lashed home an unstoppable 25-yard thunderbolt.
Despite the setback, the away side continued to press the issue but Raheem Sterling wastefully headed wide from Kevin De Bruyne's whipped free-kick and City was made to pay.
Alexander-Arnold's exquisite cross-field ball found Andy Robertson, whose sublime left-wing cross was nodded home by Salah.
Sergio Aguero tested Alisson and surprise inclusion Angelino clipped the post in an action-packed first half, while Roberto Firmino and Salah drew good stops from City's stand-in keeper Claudio Bravo.
The game was essentially put to bed six minutes after the restart when Jordan Henderson hung up a wonderful cross from the right that Mane gleefully headed in at the far post.
Sterling and Alexander-Arnold were both denied penalties before City game themselves a glimmer of hope when Angelino's low centre was drilled home, via a slight kiss of the post, from Silva.
City had Liverpool on edge again shortly after but Gabriel Jesus failed to make clean contact when Sterling had seemingly laid one on a plate.
Another claim for handball against Alexander-Arnold went unheard and Jesus wasted another golden opportunity as Liverpool saw it out to lay down a huge marker.