Liverpool FC broke the deadlock in the sixth minute when Brazil international Fabinho finished past Claudio Bravo from outside the penalty area.
The Reds extended their lead seven minutes later when Mohamed Salah got on the end of Andy Robertson’s cross before he guided a header into the net.
The Premier League leaders made it 3-0 in the 51st minute when Jordan Henderson’s brilliant cross picked out Sadio Mane at the far post.
Portugal international Bernardo Silva made it 3-1 to set up a nervous finish at Anfield but the defending champions couldn’t find a second goal.
Liverpool FC moved eight points clear of second-placed Leicester City and nine points ahead of title holders Manchester City thanks to their 3-1 win.
Former Manchester United captain Keane was full of praise for Liverpool FC after their victory over the defending Premier League champions.
“I don’t think the result will have a knock-on effect on Man City because they’ve got a brilliant coach and brilliant players,” Keane told Sky Sports.
“But the effect I think it will have on Liverpool going forward… they’re European champions and currently the best team in England. The boost to beat Man City today will be massive for Liverpool, more so than knocking Man City.
“The boost for Liverpool today will be fantastic. I don’t necessarily enjoy watching many games, believe it or not, because I’m quite critical when I’m watching football matches. But today I thought it was a brilliant game of football.”
Liverpool FC are looking to win their first Premier League title after the Reds finished in second place last term.
Jurgen Klopp’s side missed out on the top-flight crown despite collecting a club record 97 points.
Liverpool FC paid the price for failing to beat Manchester City both home and away last term after dropping five points to the Citizens.
The Merseyside outfit will return to Premier League action with a trip to Crystal Palace on Saturday 23 November.
Later on the same day, Manchester City host Chelsea FC at The Etihad as the Citizens looks to hoist themselves above the third-placed team.
Pep Guardiola’s side dropped to fourth place in the table after their 3-1 loss at Anfield.
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