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.
He scored one and was heavily involved in another two on a stellar night for youngster.
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.
Liverpool: Alisson, Alexander-Arnold, Fabinho, Henderson, Robertson (Tsimikas 85), Thiago (Shaqiri 68), Wijnaldum, Jones (Milner 68), Salah, Firmino, Mane.
Subs: Adrian, Oxlade-Chamberlain, Kabak, Tsimikas, Origi, Phillips, Neco Williams.
City have now won 10 straight Premier League games.
We are 21 games unbeaten in all competitions (5 conceded in that time) and were (last defeat November 21 by Spurs.
City have now won 14 games all competitions (4 conceded in that time) and we are in contention for four trophies.
This was our first win at Anfield since 2003.
"What was important was the three points - of course, I’m so proud of the guys who have broken a record that has stood for a long time, that shows how difficult it is and hopefully next time we can do a similar performance with people here.
"Anfield without people is completely different because I could imagine being at 1-1 and how different the influence would be on their players..
"But we reacted so well, nobody stepped back, everyone stepped forward with a huge personality. Raheem Sterling had an incredible game, like last season but a phenomenal performance.
"And the commitment from the guys in the stands who did not play supporting their team-mates. Three points and I’m grateful for this victory, but tomorrow, feet on the ground and we think about Swansea."
"We showed our courage from minute one.
"They played a brilliant game and made it difficult for us.
"We did well to play our football and keep going. We kept playing our game and in the end it paid off. Every player wants to play in a big game like this.
"I think it was definitely better in the second half. It’s something to work on to try and start well in every game that we can."
"We definitely forced the errors.
"It’s something we worked on in training to press from the front and you see the rewards in games like today. Everyone worked for each other today."
"I struck my goal perfectly, I'm happy to see it go in and to have helped the team. I enjoy it you know [playing false 9]. I like it, it’s not like you have to stay up front, you can drop in and get involved.
"I try to play there as best as I can and it’s something I need to learn. I enjoyed it, coming in and linking play in the final third."
WHAT IT MEANS...
City go five points clear at the top with a game in hand over second-placed United.
We gave extended our lead over champions Liverpool to 10 points and have played a game less.
City return to the Wembley trail on Wednesday with a trip to Swansea in the FA Cup 5th round (5.30pm kick-off).
Then it's back to the Premier League as we host Tottenham Hotspur next Saturday (5.30pm kick-off).
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