Ilkay Gundogan missed a golden opportunity to open the scoring when skied his first-half penalty into the stand, but the in-form midfielder redeemed himself with strikes either side of Mohamed Salah's spot-kick.
Ex-Liverpool star Raheem Sterling made it 3-1 when he glanced in Phil Foden's cross after another error from Alisson, before Foden put the gloss on a huge win with a clinical strike into the roof of the net.
Where to start! 10 league wins on the bounce and a first at Anfield since 2003 will make Pep Guardiola a very happy manager indeed, while City now sit five points clear at the top with a game in hand on the teams around them.
Despite a bright start, the visitors did little to make it count in the first-half, epitomised by Gundogan's squandered spot-kick. Ever the perfectionist, Guardiola will have been frustrated to see his side throw away a clean sheet, particularly with an avoidable penalty.
Manager rating out of 10
7 -- It was a bold move to start without a recognised striker as Guardiola named Gabriel Jesus on the bench, but a change in formation after the break saw his side run riot.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK Ederson, 6 -- His early clearance wasn't quite on the money as it dropped straight to Sadio Mane, but he was much more assured thereafter, although he was sent the wrong way from the spot by Salah. DF Joao Cancelo, 6 - The attack-minded full-back showed he can defend too when he did just about enough to distract Mane who headed the game's first big chance over, although he got away with one after tripping the Senegal star just outside the box.
DF John Stones, 6 -- A quieter evening than the defender probably expected, although he'll be disappointed to have seen the offside flag go up after he had neatly turned in Foden's free-kick on the slide.
DF Ruben Dias, 6 -- Treated City fans to his best impression of Gundogan when he won possession on halfway before charging into the box. He was excellent for most of the contest, but cost his side a clean sheet when he fouled Salah in the box.
DF Oleksandr Zinchenko, 7 -- His fizzed strike was comfortably blocked away to safety but the space he was given set the tone for the opening exchanges, though he struggled to marshall Trent Alexander-Arnold once Liverpool started to move through the gears.
MF Bernardo Silva, 7 -- A typically busy display from the midfielder who never shied away from his defensive responsibilities as the hosts frequently found themselves crowded out in dangerous areas.
MF Rodri, 7 -- Precision at it's finest from the Spaniard, who picked out Sterling with a mouthwatering ball out to the left that dropped straight onto the forward's boot and moved swiftly to tidy up at the other end after City gave the ball away cheaply minutes later. Solid.
MF Ilkay Gundogan, 8 -- A game of two halves if ever there was one! Having miscued his first-half penalty (and that's being generous), the German responded superbly, grabbing himself two huge goals to take his tally for the season to 11.
FW Riyad Mahrez, 6, -- Had Liverpool worried with a typical mazy run that was abruptly halted by Sadio Mane. He wasn't at his liveliest though and was withdrawn for the closing stages.
FW Phil Foden, 9 -- A breathtaking second-half from the youngster who grabbed himself a hat-trick of assists and put the game beyond doubt when he cut into the box and hammered past Alisson to make it 4-1.
FW Raheem Sterling, 8 -- The ex-Liverpool man thought he'd created the opener when he was tripped by Thiago only for Gundogan to fluff his lines from 12 yards, but the same combination was instrumental again as City opened the scoring with a move started by Sterling and finished by the German.
FW Gabriel Jesus, NR -- Replaced Mahrez in the 72nd minute as City hunted all three points, but the contest was more or less over within three minutes of his arrival, without the Brazilian having to do all that much.