Dominik Szoboszlai gave the hosts the lead with a brilliant free-kick before Bernardo Silva struck an equaliser six minutes from full-time.
City were then presented with a golden opportunity to go ahead when Alisson was judged to have fouled Matheus Nunes, allowing Erling Haaland to convert from the penalty spot in the third minute of stoppage time.
Rayan Cherki believed he had sealed the win with a late third goal, but the untidy finish was disallowed following a VAR review.
Szoboszlai brought down Haaland as the striker moved towards goal and was shown a red card, sparking anger among the City players.
After a frantic ending, City managed to protect their lead and secure all three points, completing their first league double over Liverpool since 1937.
It marked only their fourth win ever at Anfield and keeps them within six points of leaders Arsenal.
VAR controversy overshadows dramatic finale
City may have claimed a huge victory at Anfield, but the decision to rule out their third goal dominated the post-match headlines.
Under the laws of the game, Szoboszlai was deemed to have denied Haaland a clear goalscoring opportunity and was therefore sent off.
Moments after the foul, Cherki tapped into an empty net, triggering celebrations among City supporters.
However, those celebrations were cut short when referee Craig Pawson disallowed the goal and brought play back for a free-kick following a VAR check.
“After review, there is a careless foul by Erling Haaland, pulling the shirt of Dominik Szoboszlai,” he announced to the Anfield crowd.
“Before that, Szoboszlai commits a holding offence that denies an obvious goal scoring opportunity.
“The final decision is a direct free kick to Manchester City and a red card.”
City were able to see out the match and take the win, but the ruling remains a highly controversial moment that will be widely discussed.
Speaking to the BBC afterward, City manager Pep Guardiola said: “Come on referee, give the goal and go home!”
“For me, of course, the referee must apply the rules,” Haaland told Sky Sports. “But this gives him [Szoboszlai] a three-game ban.
“I feel sorry for him because he gets three matches [while denying a goalscoring opportunity is usually only one].
“I think it’s just the rules and that’s how it is, so I don’t know.
“In the end, Cherki simply passed me the ball so I could score, but he didn’t want to, so that’s what happened.”
