Liverpool have extended their lead to eight points at the top of the Premier League, with Manchester City slipping to fourth in the table.
Two first-half goals from Fabinho and Mohamed Salah, followed by a Sadio Mane header in the 51st minute meant Bernardo Silva's late strike was merely a consolation.
Story of the game
Fabinho opened the scoring for Liverpool on the six minute mark, with a fantastic strike from outside the box - marking his second goal for the Reds.
The City players were fuming claiming Trent Alexander-Arnold handled the ball the other end of the pitch moments before, but VAR stepped in and the initial decision stood.
Arguably, the opener came against the run of play as City dominated possession and started the game brightly.
Two attacks and two goals for Liverpool, though, as Salah headed home Liverpool's second of the night.
A fantastic cross-field ball from Alexander-Arnold on his weaker foot found the run of Andy Robertson.
The left back's inch-perfect cross found the Egyptian, who just about managed to stay onside to further the Reds' lead.
Sergio Aguero took City's first big chance of the game on 24 minutes with a decent effort, drawing a save from Alisson.
The Brazilian got a hand to it and punched it clear.
City kept piling on the pressure, Angelino was next to have a go for the visitors as the clock edged closer to the 30 minute mark.
The defenders’ shot deflected off the far post, a real let-off for Jurgen Klopp’s side.
It was another sucker-punch for the Manchester Club early into the second-half, however, as a fantastic cross from Jordan Henderson finds Mane.
A diving header from the Reds' No.11 sent Anfield into a frenzy as it rippled the back of the net.
Raheem Sterling penalty appeal turned down on 64 minutes as he ran the ball out of play, surrounded by Mane and Alexander-Arnold.
City had a fantastic opportunity minutes later as Sterling found Kevin De Bruyne in plenty of space out wide.
The midfielder put it on a plate for Aguero, who should tap it in from close range, but it just evades the striker to the relief of the Liverpool defenders.
B.Silva handed City a lifeline on 78 minutes after Angelino found the Portuguese international unmarked in the box.
Silva drilled it through the Liverpool backline and into the back of the net, marking their first shot on target in the second-half.
Another marginal call went against Pep Guardiola's side, the crowd suddenly becoming much nervier.
Sterling shot straight at Alexander-Arnold's hand but it was waved on my referee Michael Oliver, much to the City boss' disapproval.
Nerves soon became elation across Merseyside as the clock neared 90 minutes, "Liverpool, top of the league" ringing around Anfield as the final whistle blew.
Takeaways from the match
VAR creating more questions than answers
City players and staff were left aggrieved following shouts for a penalty early in the first-half.
The ball touched the hand of right-back Alexander-Arnold after deflecting off Bernardo Silva's hand.
Liverpool went on to score with a fantastic strike from Fabinho and VAR allowed the goal to stand, much to the bewilderment and fury of Guardiola.
It was a controversial decision, but the Premier League released the following statement: "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."
Injuries cost City
Ederson is the most recent player to join the injury list for the Premier League champions after he was substituted midweek against Atalanta.
Guardiola played a back four of Angelino, Kyle Walker, Fernandinho and John Stones with Claudio Bravo starting in goal.
Liverpool capitalised on defensive errors, as well as poor organisation and were clinical in the final third.
The Citizens didn't play badly at all, missing a number of glaring chances.
Reds go marching on
Liverpool simply refuse to waver as their unbeaten run this season continues.
Klopp will be delighted with his team's performance as the forward line punished City and the defence also put in a shift to limit the visitors to just one goal.
Question marks were put over Alexander-Arnold pre-match, but the young full-back proved why he's regarded as one of the best with a resilient defensive display, whilst also showcasing his creative flare.
Liverpool are next in action after the international break when they travel to London to play Crystal Palace on November 23.
Manchester City face a tougher test as they host Frank Lampard's Chelsea on the same day.