It was all about which of these rivals could capitalise on Arsenal’s draw at Sunderland on Saturday, who could make a statement about their intention to chase down the Premier League leaders. It was Manchester City who cleared their throats and made it plain that they are in this race for the long-haul. Liverpool barely got a word out.

The table looks a lot more appealing for Pep Guardiola and his players now, City just four points behind Arsenal and it was an occasion when they blew Liverpool away. They could shrug off the inconvenience of Erling Haaland missing a controversially awarded 13th minute penalty to put on a show of strength, particularly in the first-half.

It was Haaland, inevitably, who opened the scoring with his 19th City goal of the season and, after Nico González had benefited from a deflection off Virgil van Dijk in stoppage time before the interval, the scene was set for the coup de grace.

Jérémy Doku was almost unplayable at times, a blur of tricks and direct running and his goal for 3-0 was a beauty, a quick move inside before the perfectly executed curler with his right foot into the far corner. He merited the ovation he got when he was substituted towards the end.

Liverpool cried foul over two decisions – both driven by the VAR, Michael Oliver. They got away with the penalty when Giorgi Mamardashvili kept out Haaland’s kick but the real sickener was when Van Dijk had a header ruled out for 1-1 for an offside against Andy Robertson, who was too close to the City goalkeeper, Gianluigi Donnarumma.

The decisions were not the reason why they lost. City were slicker and more incisive; they carried the greater physical threat, too. It was hard not to fear that Liverpool’s title defence ended here and not only because they trail Arsenal by eight points. It was the manner in which they fell to a fourth away league defeat in succession for the first time since 2012. There had been no little fanfare after their midweek Champions League win over Real Madrid. They were back. Not on this evidence.

Guardiola was lauded for his 1000th game as a manager beforehand, City screening an extended and effusive tribute to him on the big screen, and then it was on to trying to unpick another of his tactical set-ups. Because the fluency, the positional interchanges of his midfielders, was really something.

City brought the intensity from the first whistle, Doku marauding from the left. Bernardo Silva sat alongside González one minute and pushed high or wide the next. Phil Foden, who had plenty of licence in the centre, allowed an early half-chance to escape him when his touch was poor.

Jeremy Doku enjoys scoring the third goal with Nico O’Reilly Photograph: Tom Jenkins/The Guardian

The touchpaper was lit by the penalty decision, the referee, Chris Kavanagh, advised by Oliver to study the replays on the pitch-side monitor of the moment when Doku seemed to run through Ibrahima Konaté before slicing back from the byline and seeing Mamardashvili come flying out at him.

The contact was minimal – one of those where you had to look very hard from a specific angle to discover it – and, if it was technically there, it did not disguise the reality that the award was soft. In the moment, Guardiola appealed for a handball against Dominik Szoboszlai, who had blocked from Rayan Cherki in the second part of the move – which felt instructive. Mamardashvili read Haaland’s intentions and went to his left to save.

City did not relent. Doku was in the mood, shimmering with menace. It was the skills, the pace, the strength; the complete package. Cherki had a shot blocked by Konaté and the breakthrough was inevitable. Liverpool were in danger of being run off the pitch. It was remarkable to see how many one-on-one duels they lost before the interval; how they plodded without inspiration.

Haaland’s goal for 1-0 was a little strange, albeit the buildup was lovely. Konaté appeared to get a little flick to Matheus Nunes’s cross from the right with Haaland airborne behind him. But the striker still managed to loop the header back into the corner of the net. How much did he know about it? Then again, it was Haaland.

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Liverpool thought they had their lifeline when Van Dijk bullied Nunes on a corner, thumping his header into the far corner. Enter Oliver – again – the VAR deeming that Robertson was interfering with the play from an offside position. By the letter of the law, it did not matter that Donnarumma looked unlikely to make the save regardless of where Robertson was standing.

Slot howled on the touchline. So did the away fans. And their wounds were salted when González tried his luck from distance and found that it was in, the shot deflecting off Van Dijk to leave Mamardashvili wrongfooted.

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Slot had stuck with his back-to-basics approach, the same lineup – broadly – that he played in the victories over Aston Villa and Madrid which had given Liverpool optimism in the buildup. The key detail was that it was the midfield three from the title-winning season last time out, with Florian Wirtz on the left of the front three. Wirtz was good, City having to resort to some roughhouse stuff to stop him.

Liverpool pushed after the restart. They made a few inroads. Ryan Gravenberch almost released Mohamed Salah, Rúben Dias forced into a saving challenge as Donnarumma made a reckless bolt from his area. González almost put through his own goal while Cody Gakpo blazed over when well-placed at the far post.

But Doku kept coming. He enjoyed himself, the alarm bells ringing loudly for Liverpool whenever he got on the ball and looked up the field. When he tricked in between Conor Bradley and Gravenberch on 56 minutes, it was another example of his twinkle-toed magic. His goal was the show-stopper. Szoboszlai would work Donnarumma with a piledriver while Salah touched narrowly wide of the far post in a one-on-one. The game was long since over.