Five nights ago, 40 miles to the north of Anfield at a remote outpost of English football, Arsenal fell to one of the most humiliating reverses of their long and august history. In the teeth of a gale that blew in off the Irish Sea, they were knocked out of the League Cup by Fleetwood Town, a team 18th in League Two.

They left with their tails between their legs, their teenage prodigy Max Dowman sent off in a melee, their heart questioned, their quality debated, their discipline an issue. Mikel Arteta and his side knew that just a few days later, at the other end of the Fylde Coast and across the Ribble Estuary, they would have to swap running the gauntlet of the Cod Army for the challenge of facing down the roar of the Kop.

They did not shirk it. If Tuesday night was a humbling, their gritty 1-0 victory in an Anfield that was a cauldron once more felt like a significant triumph. It was a defensive masterclass from the champions, an exercise in indomitability. It was their first victory here since 2012 and it took them above Manchester City so that they sit, once more, at the top of the table. Liverpool could not summon a single shot on target.

‘It felt like the end of the world when we were knocked out at Fleetwood,’ Arteta said after this win. ‘You look so silly. I was thinking “How can I lift these players up?” You have to dig deep. This was a mission to win here and it is something that we have not done for 14 years for a variety of reasons. We knew we would have to navigate some difficult moments.’

If Arteta left Fleetwood answering questions about his management of Dowman, he finished this game by striding on to the pitch after the final whistle, pumping his fists in front of the Arsenal fans celebrating in the Anfield Road end, and beating his hand on his chest. This was a vindication for him and his team. Five nights is a long time in football.

He had talked about the harsh realities of this sport after Tuesday’s loss. He had reminded everyone that playing at this level was not like ‘Disneyland’. And this victory was not like Disneyland, either. It was less a theme park and more an assault course. It was rough and it was unforgiving and Arsenal were equal to it.

Liverpool, improving under the management of Andoni Iraola, had been talked up as title contenders ahead of this match on a dank evening on Merseyside where the streets around the ground were decorated with the toothless grimaces of rotting pumpkins on doorsteps. The home team showed exhilarating signs of their re-emergence as an attacking force.

They dominated much of the game, too, but they looked like an emerging team, a team that is still evolving. Arsenal, marshalled imperiously by Declan Rice, looked like the finished article. They created one outstanding chance and Kai Havertz converted it. That was all they needed.

Their defence stayed rock-solid, although there was some puzzlement that Liverpool were not awarded a penalty for Jurrien Timber’s blatant shirt-pull on Alexander Isak. After the interval, Liverpool rarely looked like drawing level.

Kai Havertz gave the Gunners a lead to defend after finishing off a well worked move early on

The German slotted home after Declan Rice fizzed a dangerous ball across the six-yard box

Winning at Anfield was vindication for Mikel Arteta after Arsenal’s defeat by Fleetwood Town

The opening had been predictably frenetic. Neither team forged a chance but Trey Nyoni, who has forced his way into the first team with a series of excellent performances in midfield, could have been booked twice inside the first quarter of an hour.

The initial infringement was a nasty tackle on Martin Odegaard inside the first minute where he planted his studs in Odegaard’s ankle. The second was a spiteful tackle on Kai Havertz. Neither received a yellow card, which gave yet more pause for thought about the red card shown to Dowman at Fleetwood, and its aftermath.

Let’s get one thing straight – the criticism of Arteta for his ‘treatment’ of Dowman was absurd. It has come to something when a manager giving a player a hard stare is interpreted by some as a disproportionate response.

Nobody is necessarily hankering after a return to the days of Sir Alex Ferguson’s hairdrier or Joe Kinnear’s rants that broke records for expletives but if a boss is attracting censure because he looked at a player a bit funny, we are in big trouble.

Arteta is not there to indulge Dowman. He is there to coach him and to teach him and to help him grow up in the context of a Premier League football club. His actions in Fleetwood on Tuesday fulfilled his obligations in all of those criteria.

Arsenal survived the initial frenzy here and took the lead after 16 minutes. Liverpool were the authors of their own downfall. They gave the ball away from a goal kick, it was worked to Noni Madueke on the right, and when Madueke fed it to Declan Rice on the overlap, Rice crossed beautifully for Havertz, who touched it home at the back post.

Arsenal nearly returned the favour a minute later when they played themselves into trouble at the back. Bradley Barcola found himself through on David Raya but his first touch let him down and Rice moved across to clear the danger.

Alexis Mac Allister was left with his head in his hands after missing a glorious chance to score

Liverpool’s 19-year-old talent Trey Nyoni started the match but was replaced in the second half

Liverpool recovered and began to dominate the game. Barcola’s pace began to cause Arsenal all sorts of problems down their right flank and Liverpool came close to an equaliser when Virgil van Dijk flicked on a corner and Alexander Isak was denied by the brave intervention of Raya.

Arsenal were still threatening on the counter. Christos Tzolis chipped a ball to the back post and, as Liverpool scrambled to clear it, Madueke turned it back across goal. The ball was intended for Havertz, who was unmarked in the middle, but Timber could not get out of the way of it and it bounced off him into touch.

The atmosphere was febrile. Liverpool had three appeals for penalties, first for Timber’s shirt pull on Isak, then for challenges on Alexis Mac Allister and Cody Gakpo, turned down in quick succession. Tempers began to flare on the benches.

The breathlessness of the match was relentless. Florian Wirtz drove a free kick against the face of the crossbar with Raya beaten and then, three minutes before the interval, Mac Allister ran on to a cross from Milos Kerkez and, with the goal at his mercy, directed his free header too high.

Liverpool laid siege to the Arsenal goal after the break but the openings just would not come. Isak blazed high over the bar from an angle, Wirtz had a shot on the turn blocked and then, just before the hour, Dominik Szoboszlai replaced Nyoni and, to more acclaim, Rio Ngumoha came on for Gakpo.

Still Liverpool could not prise Arsenal open. Arsenal began to grow in confidence and threat. The home team The home team were grateful to Jeremy Jacquet for a clearance that prevented Odegaard turning Tzolis’s cross into an open goal, for Van Dijk’s brilliant interception to deny Havertz and, most of all, for a quite magnificent one-handed save from Alisson that diverted a Tzolis shot round the post. It will stand the test of time as one of the saves of the season.

Arsenal put in another excellent defensive display to frustrate and keep Liverpool at bay

Liverpool’s frustration boiled over. Mac Allister was booked for his part in an ugly fracas with Odegaard and Madueke. The stands became a mass of pointing fingers and shouts of protest and anger. Time-wasting and play-acting peppered the match. Liverpool felt the game slipping away in the angst.

Liverpool threw everything at it in the final minutes. Lewis Koumas flung himself at a bouncing ball but could not get enough power on his header, Ngumoha had a shot charged down, Barcola desperately searched for pockets of space but could not find them. There were six minutes of time added on but there was no way through. Arsenal’s defence would not yield.

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