City missed a first-half penalty before two Ilkay Gundogan goals - with a Mo Salah penalty sandwiched in-between - and further goals from Raheem Sterling and the irrepressible Phil Foden completed the rout.
It's 14 wins on the bounce for this talented, hard working group of players and 21 games unbeaten - and for once, it was a very happy trip home from the home of Liverpool FC.
City started confidently without creating too many chances in a game that was all about pressing, breaking up play and trying to impose styles.
There were tactical battles all over the pitch, but not much in the way of goalmouth action.
Raheem Sterling had a few attempts at getting past Trent Alexander-Arnold on the left, and when he finally did get past, Fabinho caught his leg as he moved into the box and referee Michael Oliver pointed to the spot.
If there was ever anyone you’d back to score given his form of late, it was Gundogan so when he stepped up and put his shot over the crossbar, a golden opportunity had been missed.
Liverpool showed flashes of menace but the first-half ended in stalemate.
But just four minutes after the restart, City were ahead.
Great work from Phil Foden allowed Sterling to again burst into the box and as he returned the pass to Foden the youngster's low shot was parried by Alisson and Gundogan fired the loose ball into the roof of te net.
It was a huge relief for the German who has been practically flawless for the past few months.
But on 63 minutes, a rare mistake by Ruben Dias saw Mohamed Salah nick the ball and as he moved into the box, he made the most of Dias' attempt to recover and the referee awarded a penalty.
Salah scored a confident spot-kick and City were suddenly facing a much trickier final 25 minutes or so,
No matter, in the next attack City took the lead again after a couple of mistakes by keeper Alisson saw the ball fall to Foden on the right of the box and he squeezed through two challenges before crossing for Gundogan who couldn't miss from a couple of yards out.
And three minutes later, Alisson again made a howler, trying to pass out from the back he gave it straight to Bernardo who drew the keeper off his line before chipping to the back post where Sterling gleefully headed home from a yard out.
And it got better still on 83 as the devastating Foden again took on the Liverpool defence, cutting in from the right before firing an unstoppable rocket of a shot into the top left corner to make it 4-1.
What a goal and what a performance by a player who is getting better and better.
But it was a superb all-round display by a team who has now won 14 matches on the bonce.
HUGE STATEMENT BY CITY
To go to Anfield and dismantle Liverpool is just about as good as it gets.
But City will relish this victory for so many reasons.
Two wins in 65 years, this was overdue and then some, but while the fact the empty stadium clearly affected the hosts more than the visitors, City were just too good.
And in Phil Foden, we have one of the best young players in the world.
CITY’S PENALTY WOES
For a team with perhaps the best technique in the Premier League, City struggle to score penalties.
That’s three penalty misses against the Reds – and misses as in missed the target completely – and in games like this, it can be so costly.
Perhaps we’ve been spoiled in the past with Mario Balotelli and Yaya Toure, but one player who does score regularly from the spot is Sergio Aguero.
Maybe there is an expert taker in the side that we don’t yet know of – only time will tell.
Fortunately, on this occasion, it didn't matter.