Erling Haaland made amends for an early penalty miss by heading City into a 29th-minute lead, before Nico González doubled the advantage with a deflected strike just before half-time. Jeremy Doku then capped a superb individual display by sealing the win with a brilliant effort in the 63rd minute.
City dominated possession from the outset, with Doku their most creative outlet as he repeatedly drove into the Liverpool box. Mohamed Salah had an early chance for the visitors, but his effort failed to trouble Gianluigi Donnarumma in the City goal.
Doku continued to cause problems, threading a superb pass through Liverpool's defence that Phil Foden was unable to convert. Moments later, the Belgian winger was brought down in the box by Giorgi Mamardashvili, and after a VAR review, a penalty was awarded. However, Haaland's effort from the spot was saved by the Liverpool goalkeeper, keeping the score level.
Liverpool began to find their footing in patches, with Rayan Cherki seeing two efforts deflected wide. Yet City remained the more dangerous side, with Doku forcing Mamardashvili into a sharp near-post save before Haaland broke the deadlock on the half-hour mark — rising above Ibrahima Konate to nod home a deep cross from Matheus Nunes.
Liverpool thought they had equalised soon after when Virgil van Dijk powered a header into the bottom corner, but the goal was ruled out for offside, with Andy Robertson adjudged to have interfered with play.
City punished the visitors further deep into first-half stoppage time, as Gonzalez's strike took a wicked deflection off Van Dijk and wrong-footed Mamardashvili to make it 2–0.
Just two minutes into the second half, Doku almost added a third, stretching to meet a Nico O'Reilly pass but narrowly missing the target. Pep Guardiola introduced Savinho for Cherki on 53 minutes to maintain his side's attacking edge, while Arne Slot responded with a double substitution — Cody Gakpo replacing Hugo Ekitike and Milos Kerkez coming on for Robertson.
There was a brief scare for City when González's attempted clearance looped onto the top of his own net, before Gakpo fired just over from the edge of the box. But it was Doku's night, and the Belgian winger put the result beyond doubt with a stunning curling strike into the far corner midway through the second half.
With the points secured, Guardiola replaced Doku with Omar Marmoush, while Curtis Jones came on for Alexis Mac Allister as Liverpool sought a late response. Dominik Szoboszlai forced Donnarumma into a fine save from distance, and Salah missed a golden chance with ten minutes remaining, clipping his shot narrowly wide of the post.
It proved too little, too late for Arne Slot's side, who slumped to their fifth defeat of the season. The result leaves Liverpool eighth in the Premier League table, while Manchester City move up to second on 22 points — four behind leaders Arsenal.
Manchester City secured a second successive Premier League victory at home against Sunderland, Chelsea were held scoreless away to Bournemouth while Tottenham managed to beat Brentford.
Manchester City manager Pep Guardiola insists his side are moving in the right direction as they continue to evolve following an off-season of significant rebuilding.
Arne Slot has admitted that Liverpool "need to do better" at bringing Alexander Isak into dangerous areas after another quiet outing for the Swedish forward in Wednesday's 1-1 draw with Sunderland.
Liverpool were held to a 1-1 draw by Sunderland at Anfield after a late own goal rescued a point for the Premier League champions.
