Second-half goals from Erling Haaland, Jeremy Doku and Rayan Cherki extended City’s flawless start under Enzo Maresca after Ryan Gravenberch had been sent off for two yellow cards.
City re-established their three-point lead at the top of the table, but the future of any title challenge rests on the outcome of the club’s appeal against widespread financial impropriety.
“We need to learn how to deal with the outside noise, but make our own noise, which is to win games,” said Maresca.
“Our fans were singing at the end, so the noise was from us.”
An independent commission found City and their Emirati owners arranged “sham” deals to artificially inflate revenues and reduce costs by more than £900 million between 2009 and 2018.
No sanction has yet been handed down, but a severe points deduction or even expulsion from the English top flight are on the table unless City overturn the decision.
There has even been speculation there could be retrospective action to strip titles.
“The uncertainty is not good for anyone,” said Liverpool boss Andoni Iraola.
The multiple breaches of Premier League laws came during a period in which City won three titles and a clutch of other trophies.
City’s rivals believe, however, that the illegal spending during that period also built the foundations for a golden era under former boss Pep Guardiola, who left at the end of last season.
Liverpool were one of the clubs most affected, having finished second to City three times in the past 12 years.
“City have fundamentally cheated to win those leagues,” Jamie Gallaghie, a 48-year-old teacher, told AFP.
The visitors arrived under the protection of a police escort with a hostile Anfield welcome expected, but there was no repeat of the violent scenes when their team bus was pelted by bottles ahead of a Champions League clash in 2018.
Liverpool fans lined the streets to greet the City players with chants of “cheats” and “going down”, while merchandise stalls were littered with flags and scarves mocking their rivals’ financial scandal.
In the iconic Kop end behind one goal a banner read “a generation of supporters cheated.”
The battles between Guardiola’s City and Jurgen Klopp’s Liverpool in recent years became the Premier League’s marquee event.
But with the eyes of the world watching, Liverpool failed to rise to the occasion on the field.
New Liverpool boss Iraola’s options were blunted without the injured Dominik Szoboszlai, Alexander Isak and Cody Gakpo as the Spaniard suffered his first defeat since taking charge of the Reds.
An Abu Dhabi-backed takeover in 2008 transformed City from mid-table mediocrity into the dominant force of the English game.
City’s economic might was on full show and helped turn the game as Maresca could introduce Doku off the bench early in the second half.
Within minutes the Belgian winger had been chopped down by Gravenberch, who was shown a harsh second booking, and Liverpool never recovered.
Doku’s deflected shot was then smashed home by Haaland to break the deadlock 25 minutes from time, opening the floodgates.
Three minutes later Doku curled a sensational strike into the top corner himself.
Cherki then exchanged a slick one-two with Josko Gvardiol before slotting under Alisson Becker to rub salt in Liverpool wounds.
The defeat leaves Liverpool nine points adrift of the leaders down in ninth. (AFP)