Liverpool took a huge advantage in the Premier League title race as their 3-1 win opened up a nine-point gap over opponents Manchester City.
Leicester, eight points behind, are now their closest challengers after City's miserable run at Anfield - one win in 29 visits - continued in a match which left Pep Guardiola raging at some controversial VAR calls.
Fabinho could not have timed his first goal since December any better with the sixth-minute opener, with City still arguing for a handball by Trent Alexander-Arnold in the other penalty area, and Mohamed Salah and Sadio Mane put the game out of sight before a late consolation for Bernardo Silva.
Liverpool have now faced all their big-six rivals plus Leicester, while City have plenty of work left to do having only met the Reds and Tottenham up to this point.
In a truly bizarre opening 20 minutes, City dominated to the extent their hosts barely had a chance to string more than a couple of passes together - yet when they did it was so devastatingly effective it made any possession statistics irrelevant.
Straight from kick-off City sent the ball deep into enemy territory, pressurising so much in there that their opponents did not complete a pass and conceded a corner in the opening 60 seconds.
That pattern was replicated for the first quarter of the game, but the more City pushed the more their suspect defence was left exposed to the tranche of space opening up around them.
There was little doubt there would be a VAR controversy in this most high-profile of games and it came just six minutes in.
A cross from Kevin De Bruyne, playing almost as high as a second striker, deflected up off Bernardo Silva's arm and hit Trent Alexander-Arnold's outstretched limb.
With referee Michael Oliver waving away penalty claims Liverpool broke, with Mane charging into the box, and when Rodri's half-clearance reached Fabinho he drilled home an unerring 25-yard shot which barely got above three feet off the floor as it whistled inside Claudio Bravo's right-hand post.
If that was good even better was to follow with the quality of Alexander-Arnold's crossfield left-footer to Andy Robertson, the defender's curling cross and Salah's stooping header all to be admired.
VAR ruled Salah had been just behind John Stones and the goal stood and Liverpool were firmly in the driving seat, both in this match and the title race.
City responded with a Sergio Aguero shot which Alisson Becker palmed away and an Angelino effort, having run onto De Bruyne's through-ball, which deflected off Virgil Van Dijk and hit the far post.
Aguero also guided a shot wide of the same post after De Bruyne slipped the shackles of Fabinho.
Liverpool were far from shrinking into their shell, however, and Bravo saved from Firmino after Alexander-Arnold's 60-yard run, while also denying Salah.
Mane struck the killer blow six minutes after the break when Bravo, caught under a whipped Jordan Henderson cross, could not keep out the Senegal international's far-post header.
Raheem Sterling, who has not enjoyed many happy returns since leaving Anfield in 2015, continued his one-man mission to drag his side back into the game and when he cut in from the left it took a sliding Dejan Lovren to deflect over his shot.
The former Reds winger was furious not to get a penalty after Mane's hand on his back, but again VAR backed Oliver's call and Liverpool began to think it was their day when Aguero - who has yet to score at Anfield in his career - completely missed De Bruyne's cross six yards out.
Silva beat Alisson at his left-hand post from Angelino's cut-back with 12 minutes remaining to deny the Reds their first home league clean sheet of the season and Sterling's square pass then missed everyone in the penalty area as City started to take advantage of tiring Liverpool legs.
City had another penalty shout denied when Sterling drilled a shot at Alexander-Arnold's hand and Guardiola furiously signalling "twice" to fourth official Mike Dean highlighted the level of the visitors' frustration at decisions not going their way.