Jurgen Klopp’s side took the lead through a Fabinho rocket in the sixth minute, before Mohamed Salah headed home to make it 2-0 shortly afterwards.
Both goals were controversial for different reasons. City felt they should have been awarded a penalty moments earlier following an inadvertent Trent Alexander-Arnold handball, while there were suspicions that Salah may have been offside when he scored from Andrew Robertson’s cross.
Another Premier League game-week and yet more VAR controversy.
Sadio Mane then killed the game off with a third goal shortly after half-time, while Bernardo Silva's goal with just under 15 minutes proved to be nothing more than a consolation as City ended the game on top.
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The result leaves Liverpool eight points clear of Leicester City and Chelsea in second and third place, respectively. City, meanwhile, stay in fourth place but now find themselves nine points behind the league-leaders.
Pep Guardiola’s men actually started the game on the front foot but the turning point came in the fifth minute when Sergio Aguero and his teammates were left screaming for a penalty when the ball hit Alexander-Arnold’s outstretched arm.
The VAR did not believe the incident warranted a penalty and play was subsequently allowed to continue. Liverpool went up the opposite end of the pitch and took the lead thanks to Fabinho’s pile-driver from range.
A statement from the Premier League about the first goal read: ”The VAR checked the penalty appeal for handball against Trent Alexander-Arnold and confirmed the on-field decision that it did not meet the considerations for a deliberate handball."
Raheem Sterling, who received plenty of stick from the Liverpool fans who once cheered his name, then spurned an immediate chance to equalise, heading over from a free-kick.
It proved to be a costly miss. Liverpool doubled their advantage in the 13th minute thanks to Salah’s clever headed finish.
Despite suggestions that Salah may have been offside when Robertson whipped the ball in, Sky Sports confirmed later in the half (following a significant delay) that the Egyptian forward was played onside by John Stones.
Claudio Bravo made a couple of saves before the half-time interval to prevent Liverpool from extended their lead, but City’s second-choice goalkeeper was powerless to prevent Mane’s header from beating him in the 51st minute.
Jordan Henderson’s superb cross was met at the back post by the red-hot Senegalese winger.
City thought they should have been awarded another penalty when Sterling went down inside the box following contact from Mane. Once again, though, VAR ruled in favour of the Reds.
And when Aguero missed a sitter with just over 20 minutes remaining, City knew for certain that this wasn't their day.
Liverpool didn't end the 90 minutes with the clean sheet intact, however. Silva's neat finish beat Alisson Becker at his near post to give the travelling City supporters something to cheer.
The visitors, to their credit, worked hard during the closing stages in an attempt to rescue something from the game.
Guardiola felt City should have had (yet another) penalty and expressed his frustration on the touchline.
But no further goals were scored and it's hard to see Guardiola's side catching Liverpool from this position, even though it's still early in the season.
Expect more twists and turns between now and May but Liverpool will never have a better chance to end their long wait for a Premier League trophy.
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