The victory, sealed with goals from Fabinho, Mohamed Salah and Sadio Mane, leaves unbeaten Liverpool on 34 points from 12 games.
They are eight points ahead of Leicester City and Chelsea, and nine in front of Pep Guardiola’s fourth-placed Manchester City who are the competition’s defending champions.
While talk of decisive results in November, with 26 games of the campaign remaining, is premature, the manner of Liverpool’s win was instructive.
It was over a team which has dominated the league for the past two seasons was certainly a declaration of intent.
“The boys were completely focused and concentrated. It was so good,” Liverpool manager Juergen Klopp said.
Anfield exploded when Liverpool grabbed a sixth-minute lead with a thundering drive from Brazilian Fabinho.
He had pounced on a poor clearance from Ilkay Gundogan and blasted past Claudio Bravo from over 20 metres out.
Yet Manchester City felt the stunning effort should have been ruled out — and a penalty kick awarded to them.
This was because before the break leading to the goal Liverpool defender Trent Alexander-Arnold appeared to handle the ball inside the box, but the VAR review went against the visitors.
It was the latest VAR controversy in the Premier League and is certain to spark more debate.
But while the opening goal set the tone, Liverpool’s dominance was soon evident all across the field.
Manchester City pushed forward in response and Raheem Sterling missed a close-range header.
But Liverpool struck again in the 13th minute when Andy Robertson crossed from the left and Salah nodded the bouncing ball past Bravo to make it 2-0.
Juergen Klopp’s European champions, without a domestic league title since 1990, now had a firm grip on the game.
They caused constant trouble for Manchester City’s shaky defence with their powerful surges forward.
Liverpool were on top physically and their pressing stopped Manchester City from establishing their usual possession game, but still they managed to carve out some openings.
Sergio Aguero, who had a disappointing game, forced Liverpool goalkeeper Alisson Becker into action in the 25th minute.
Then the Argentine should have done better three minutes before the break when he shot wide after being fed by Kevin De Bruyne.
Guardiola needed to adjust something at the break to find a foothold in the game.
But Manchester City’s third defeat of the season, after losses to Norwich City and Wolverhampton Wanderers, was assured when Liverpool made it 3-0 six minutes after the interval.
Jordan Henderson superbly worked space on the right flank and whipped in a cross which Mane dived to head home at the back post.
Bernardo Silva pulled a goal back for Manchester City in the 78th minute, drilling home a low cross from Angelino and the visitors enjoyed some late pressure.
But it was too late for a comeback from the champions.
Manchester City have not won at Anfield in the league since May 2003 —- their only win at Liverpool in 38 years, but manager Pep Guardiola took positives from Sunday’s performance.
“It’s not easy after being two goals down to react the way we reacted. It was one of the best performances I have ever seen from my team.
“That’s what we needed and hopefully we can continue to make the steps we need,” he said.
“You saw in the last 10 or 15 minutes when City scored the goal it gave them mental belief and from that moment they controlled the game,” Klopp, whose side have an eight-point lead over Leicester City and Chelsea, said.
“But the other 70 minutes we controlled the game with our intensity and didn’t let them do what they wanted. If that was so easy a lot more teams would try it, but the boys put in an incredible shift again.”
Klopp, whose side are now unbeaten in 29 Premier League games, said all three goals were “incredible”.
“That’s what you need on a day like this. You have to score special goals against them, and you have to defend with your heads which is what we did,” he said.
“I don’t know many ways to beat City but if we want to do it we have to do it with intensity and with forcing them into our game and that’s what the boys did today.”
Klopp said he could understand opposite number Pep Guardiola’s frustration with the opening goal when Fabinho lashed home on the counter-attack after Liverpool defender Trent Alexander-Arnold appeared to have handled in his own area.
“I didn’t see it,” he said. “People told me it hit Bernardo Silva’s hand then Trent’s. If Bernardo had scored with his hand it would have been disallowed, wherever the hand was.
“I understand how disappointed they are, we would feel exactly the same, 100 percent. But on the other hand the reaction we showed seconds later in front of their box.”
While admitting Liverpool were now in new territory with such a lead, Klopp said they might need every point.
“Each point we have we need to go through the most intense period ever,” he said.
Alexander-Arnold described the win as a “massive three points” while fellow full back Andy Robertson said the opening goal had been crucial to the outcome.
“We didn’t start the best. I think they had two corners inside the first minute so it was always going to be an important factor,” he said.
“Now it’s all about keeping it in perspective. We’ll see where we are after Christmas and the busy period coming up.”