The home side gave an early signal of their intent when Roberto Firmino put Sadio Mane and although his control was poor the ball came to Mohamed Salah, whose strike was blocked.
But it took only nine minutes for their high-octane start to be rewarded with the opening goal, Alex Oxlade-Chamberlain getting away from Fernandinho before thumping home a low finish from 20 yards.
Kevin De Bruyne tried to muster a fast response from the visitors but delayed his pass to former Liverpool winger Rahem Sterling, booed by the home fans throughout, and he was offside by the time the ball arrived.
But the opening stages were being dominated by Jurgen Klopp's Liverpool and Salah shot wide after 15 minutes following a fluid breakaway before De Bruyne was again involved as his dangerous cross fizzed just beyond Sergio Aguero.
City, however, began to hit their stride and came close when Leroy Sane's shot deflected narrowly wide and then De Bruyne again looked for Aguero with a pass that was clutched by home keeper Loris Karius.
With half an hour gone, City had to take off Fabian Delph, who had a knee problem, replacing him with Danilo and soon afterwards Firmino headed wide from a difficult angle for Liverpool.
But with four minutes remaining until the break, Sane levelled for the Premier League leaders, controlling a pass from Kyle Walker and getting past Joe Gomez before firing an angled strike past Karius, who could have done better.
City began the second half on the front foot and, after Aguero had seen a shot blocked, Nicolas Otamendi saw a header from a corner clip the Kop end crossbar on its way over.
That, however, turned out to be the prelude to an astonishing spell of attacking that won the game for Liverpool.
The home side led after 59 minutes when Firmino got the better of John Stones and, one-on-one with keeper Ederson, clipped a superb finish over him and in off the post.
After 62 minutes, with City rocking, it was 3-1 as Mane blasted home after the visitors had lost the ball in their own half and Salah had found him in space on the edge of the area.
And within five minutes a fourth goal had flown past the shell-shocked Ederson, whose attempted clearance was stopped by Salah, 40 yards out, and he took one touch before lifting a stunning finish over the stranded goalkeeper.
Bernardo Silva replaced Sterling after 71 minutes and pulled a goal back for City with six minutes remaining, smashing past Karius after a loose ball had fallen to him.
It seemed too little, too late -- but although Ilkay Gundogan scored another in the first of four added minutes, Liverpool held on.