Mohamed Salah scored the only goal of the game at Anfield as Liverpool condemned Manchester City to their first defeat of the Premier League season.
The Egypt international grabbed the winner with a lightning-quick goal which caught City cold.
Goalkeeper Alisson Becker's quick ball out from the back had Salah on the move, allowing him to expose Joao Cancelo one-on-one 15 yards inside the opposition’s half.
When the offensively-minded defender tried to nick the ball, Salah rolled him, raced away and confidently struck an 11th goal of the season.
But City had been left fuming at referee Anthony Taylor before Salah's goal after he disallowed Phil Foden's strike early in the second half after a VAR review.
Tensions boiled over late on with Reds manager Jurgen Klopp sent to the stands for his overzealous protestations against a foul he felt his side should have been given.
The final pass was lacking for the visitors, though, as Liverpool held on for just their third league win of the season to move up to eighth in the table on 13 points. They are 10 behind second-placed City, who trail leaders Arsenal by four points.
“It takes a lot to get the three points,” said Liverpool defender Virgil van Dijk. “It was always going to be very intense. First half I think we played quite well and we didn't give much away.
“Second half we had to defend a bit more but we won and that is the most important thing.
“For both sides it is a lot of running, a lot of communication and who wanted it more. We showed a lot of fight.
“If you drop a slight percentage they will punish you. It was important to get the clean sheet.”
The first half was entertaining without being truly exciting as Liverpool defied their recent troubles and not only took the game to their opponents but controlled it for large periods.
That did not mean City were not without their threat and Erling Haaland was presented with a few half-chances and would have been disappointed not to score from two far-post headers from Kevin De Bruyne crosses.
Liverpool had only one effort on target in the opening 45 minutes but Diogo Jota could also have done better with his header he directed straight at Ederson from Harvey Elliott’s cross.
But what was apparent from this performance which was not on a number of others this season was Liverpool’s willingness to put in a shift.
The 19-year-old Elliott, preferred to captain Jordan Henderson in midfield, has been criticised for his lack of defensive capabilities but his awareness and discipline were a feature which were replicated in other areas.
Van Dijk finally looked like the world-class defender of old, marshalling the backline with calmness and authority. But City cannot be kept quiet for too long and the second half was a far more open affair.
Elliott and Roberto Firmino combined to send Salah haring through and he outpaced Nathan Ake but what looked like a certain goal was denied by the faintest of touches by Ederson, not spotted by Taylor who awarded a goal-kick.
Then the controversial moment of the match. Haaland shrugged off Fabinho to set up the move which saw his shot saved by Alisson, only for Foden to force home the rebound past Joe Gomez on the line.
Liverpool’s players were incensed as they felt the Norway international had fouled Fabinho in the build-up and the Norwegian also appeared to take the ball out of the goalkeeper’s hands – and VAR official Darren England agreed, sending Taylor to the monitor to reverse his decision.
City manager Pep Guardiola was apoplectic at the outcome. “The referee said played on, played on, played on, there were a thousand million fouls like this and this one is because we scored a goal,” said the Spaniard. “So they disallowed because we scored a goal, otherwise it would not have been disallowed.”
Jota heading over from Salah’s cross gave him more cause for concern soon after as the atmosphere stepped up a notch – and so did City’s intensity, with Alisson sticking out an arm to deny Haaland again.
Klopp’s substitutions, three of them in the 72nd minute, were positive, with Darwin Nunez, Fabio Carvalho and Jordan Henderson coming on and Salah getting some new instructions from his manager.
Whatever he said it was effective as within four minutes the Egypt international had breached Ederson’s goal in front of the Kop with the perfect counter-attacking move to send Anfield wild.