Reds goalkeeper Alisson endured a nightmare second half on Merseyside, while Ilkay Gundogan scored twice after an earlier penalty miss, Raheem Sterling notched a header and the excellent Phil Foden netted a sensational late goal as dominant City won at Anfield for the first time since 2003.
An emphatic triumph means City now sit five points clear of nearest challengers Manchester United at the top-flight summit with a game in hand.
Meanwhile, Liverpool – who also lost at Brighton in midweek – stay fourth and are now 10 points off the top after back-to-back defeats and another hammer blow to their title defence.
What began as a highly-tactical battle by two highly-drilled teams was ultimately settled by individual errors.
Liverpool boss Jurgen Klopp, who suggested earlier in the week that City had benefited from a two-week break over Christmas due to the coronavirus pandemic, brought back Alisson, Fabinho and Sadio Mane, while Guardiola opted to go without a recognised centre-forward, dropping Gabriel Jesus to the bench with Foden handed the false nine role.
It was an intriguing decision considering Liverpool were playing midfielders Fabinho and Jordan Henderson in a makeshift central defence but the City manager was more concerned with winning the midfield battle.
That was where most of the match was played but early on it was the hustle and bustle of press and counter-press with City’s outstanding defender Ruben Dias the most obvious victim, once giving the ball straight to Salah and then also passing it straight out of play.
Mane should have done better with his header after Trent Alexander-Arnold had weaved himself some space on the right while Roberto Firmino’s volley was tipped over.
The first run of any purpose from Sterling, stationed out on the left, won the penalty as he skipped past Alexander-Arnold and caught the trailing leg of Fabinho – only for Gundogan to blaze the spot-kick into the empty Kop.
The German made up for his failure five minutes after the break when he rifled home from close range after another Sterling incursion into Liverpool’s penalty area allowed Foden a shot which Alisson could only parry.
Curtis Jones saw a shot deflected wide but with City in the ascendency it appeared Liverpool were drifting out of the game, seemingly clinging on at times.
However, they won a penalty of their own when Dias lost possession on the edge of his own area and brought down Salah, who picked himself up to succeed from the spot where Gundogan had failed.
It was the Egyptian’s 22nd goal of the season, only one fewer than he managed in the whole of the previous campaign.
John Stones had a goal ruled out for offside before the hosts twice shot themselves in the foot from the boot of the usually reliable Alisson, with Foden cutting in from the right to apply the coup de grace with seven minutes remaining.
Not only did it inflict the heaviest home defeat of Klopp’s reign but it also meant it is the first time since 1963 Liverpool have lost three successive home league matches.