For 80 minutes, if plenty were perplexed by an outbreak of extraordinary entertainment, maybe no one was more confused than Erling Haaland. There had been seven goals, but he got none of them. A giant figure in the No 9 shirt scored a hat-trick, but it wasn’t him. By the end, there were two outcomes Haaland recognised only too well. Manchester City won and he had scored.

But they were the only normal elements of an astonishing afternoon. Enzo Maresca’s side extended their 100 per cent start, but in unusual fashion. “I prefer to win 1-0 than 5-3,” said the Italian. He did not get his wish. He had predicted Sunderland would be City’s toughest match of the season so far; he was right in that part, at least.

“Sunderland [against] Arsenal last week was another crazy game,” noted Maresca. The Black Cats have put in colossal efforts against the two title favourites, in contrasting fashion, but with nothing to show for either whereas City are the big winners of this weekend at the summit. They and Arsenal both conceded three. The difference is that City scored five.

It took Haaland to put enough distance between themselves and Sunderland, a side who mounted not one comeback but a series. The first time Sunderland trailed, they levelled after three minutes, the second after four. Seven minutes after they went behind for a third time, Brian Brobbey’s deflected shot looped on to the bar. He instead completed the rarity of a hat-trick against City two minutes after they scored their fourth.

Ruben Dias was required to hook the ball off the line to prevent Sunderland from levelling it up at 4-4. Even at 5-3, Dan Ballard hit the post. Sunderland had 17 shots, eight on target and an xG of 4.25. “We probably deserved to score two or three more,” said manager Regis Le Bris.

All of which felt more incongruous given the reality that Sunderland had not scored more than once in a game so far this season, or that City had arrived on a run of four consecutive clean sheets.

But then, at kick-off, Antoine Semenyo had yet to score this season and he got two goals. Brobbey was still awaiting his first goal of the campaign and, within an hour, he had become the first player to get a Premier League hat-trick against City since Jamie Vardy six years ago; before that, no one had since Vardy again in 2016.

The Dutchman made history, and it counted for nothing. Not since Roque Santa Cruz in 2007 had anyone got a Premier League hat-trick in a losing cause. Perhaps it will be scant consolation to Sunderland, too, that they fashioned the game of the season so far. “A defeat but we are proud,” added Le Bris.

“We found a way to win,” said Maresca. Haaland was overshadowed, but added another distinction to a long list. He has now scored against all 25 clubs he has faced in the Premier League, though only after initial frustration. On the stroke of half-time, he had rolled a shot wide of an unguarded goal. When he converted Josko Gvardiol’s low centre, the flag was raised. Haaland, famously, is never offside, but VAR proved Gvardiol was not, either. For the second successive Sunday, a Haaland goal from a Gvardiol cross was given after the intervention of technology. This one is less likely to prompt an apology from Howard Webb.

Sunderland wanted a penalty for a possible handball by Elliot Anderson. City had other concerns. “Two of the three goals we conceded were too easy,” said Maresca. They did not defend like possible champions, though maybe that reflected the unique threat of the bruising Brobbey. They – Dias in particular – were battered and bullied by the target man, who was aided by the sleek creativity of Enzo Le Fee and the raw pace of Nilson Angulo.

Yet while Maresca has packed his side with centre-backs, City look fragile. Brobbey’s first goal of the afternoon and the campaign stemmed from Le Fee’s pass, enabling him to power between Ruben Dias and Matheus Nunes. His second came when he was given an open goal after Thomas Meunier sprang the offside trap to centre.

City’s back four were caught out by runners again for the third: Granit Xhaka chipping the ball over the defence, Angulo touching the ball to Brobbey for a tap-in. “I am really pleased for him,” said Le Bris. “We were not concerned he didn’t score in the first four games.”

Brobbey showed his potency and City displayed theirs. The scoring was begun by an audacious free kick from an acute angle, executed superbly by Enzo Fernandez. Their advantage was restored when Rayan Cherki drove in a shot after Iliman Ndiaye had won the ball in midfield.

Semenyo’s double could come with regrets for Sunderland: the first a shot drilled through the legs of Kevin Danso, the second when Cherki’s pass bounced off two Sunderland defenders, falling obligingly for the winger to finish.

He never scored in a loan spell for Sunderland. He got a double against them. It was that kind of day.