With this win, Liverpool consolidated their position on the top spot, with 34 points, eight clear of Leicester City in the second, while City drop to fourth with 25 points.
Here is how the match unfolded.
Liverpool on top as they quickly go up 2-0
The hosts were in control right from the opening whistle and it did not take them long to score.
Six minutes into the game, Sadio Mane gifted a beautiful cross to Fabinho to drive it home.
Seven minutes later, fans witnessed beautiful gameplay by Trent Alexander-Arnold and Andy Robertson. Their combination helped Mohamed Salah to put his name on the score sheet.
City up the ante before half-time
The second quarter saw City coming close on several occasions, as Sergio Aguero's powerful effort from inside the box in the 25th minute was saved by Alisson.
Four minutes later, Angeliño just tapped it inches wide.
The 37th minute saw a good effort from Roberto Firmino getting denied by Claudio Bravo. And then, six minutes later, Aguero's 18-yard-long effort went wide once again.
Liverpool pull of third as the intensity continued
Following the half-time, Liverpool continued with the same intensity, as it was in the 51st minute when Jordan Henderson was left unmarked by İlkay Gündoğan, who delivered a perfect cross for Mane to head in for the third.
Two minutes later, it was City, as Sterling dribbled past Alexander-Arnold for a powerful shot, only to be deflected by Dejan Lovren, inches over the crossbar.
City strike back but lose the game
The final quarter saw the visitors going for relentless attacks, as Bernardo Silva fired in the cross from Angeliño in the 78th minute to score the first for City.
Two minutes later, Sterling discharged a pass to Gabriel Jesus, only for Virgil van Dijk to clear the ball away.
The 84th minute saw de Bruyne head a cross over the bar.
Some key stats from the match
Here are some key stats from the match:
Fabinho scored Liverpool's ninth goal of the season from outside the box, more than any other EPL side.
City trailed by three goals for the first time since January 2018, which too was against Liverpool.
It's the first time since September-October 2014 when Liverpool have conceded in nine consecutive matches.
Liverpool almost emulating Manchester United of 1993-94
8 - Liverpool have won 11 of their first 12 Premier League games this season and lead the table by eight points – only Manchester United in 1993/94 have had a bigger lead after 12 games of a Premier League season (nine points). Outstanding. #LIVMCIpic.twitter.com/YL9d09qMxY