The Reds started the game slumped in 12th place, but are now up the eighth after taking all three points from the reigning champions.
Man City remain in second, level on points with Tottenham, with Arsenal now four points clear at the top of the table.
Mo Salah scored the only goal of the match in the second-half, but there easily could have been several more goals for both sides.
City threatened in the first-half, coming closest through Erling Haaland in the 36th minute, but the hot-shot striker missed his mark from close range.
It wasn't long into the second-half before City thought they'd broken the deadlock through Phil Foden, but the goal was ruled out.
After a VAR consultation, referee Anthony Taylor deemed Fabinho had been fouled in the build-up play and chalked the goal off the scoreline.
This decision sparked something in the City squad, as they then fiercely fought back against the hosts, who were arguably already on the back foot.
Liverpool took the lead through Salah in the 76th minute, though, as Alisson found the Egyptian with a long-range pass straight out of his gloves.
The Reds' No.11 made no mistake from close range after beating down the pitch toward Ederson's goal.
With less than five minutes on the clock, manager Jurgen Klopp was shown a red card for animated protests to the officials.
Unfortunately, Diogo Jota was withdrawn before the full-time whistle with a suspected injury. Further information on his condition is expected in due course.
