Arsenal ended a 12-year wait for a Premier League win at Anfield and took a huge stride, even at this early stage, towards defending their Premier League title while surely slamming the door on any potential Liverpool charge.

Even without the elephant in the Manchester City room, the defending champions are going to take some stopping now.

1. A huge win for Arsenal, one that cements their status as clear favourites to defend their Premier League title even if Manchester City do get to keep hold of all the points they win – and they have stopped winning points at an injudicious time.

It’s a win that also prevents Liverpool from inserting themselves into that conversation. The chance to cut the gap at the top to three points has instead seen that number balloon to nine.

In this league, it’s just not possible to imagine Arsenal will shed enough points to allow even a flawless Liverpool to reel in such a gap. And Liverpool, as they showed here, are simply not a flawless side.

2. Nor are Arsenal, but they remain a staggeringly effective one. They were fortunate to walk off with a 1-0 lead at half-time. But thoroughly deserved it by the final whistle.

In the first half, Liverpool successfully dragged Arsenal from the order that they crave and in which they are so serenely comfortable into a game of chaos and nonsense. Liverpool do deserve credit for this, because very few teams manage that. But they couldn’t sustain it.

A roaringly entertaining first half full of vim and vigour raced by in a flash. But Arsenal strangled all the life out of it in the second half. It was much less entertaining, much less enjoyable as a spectacle, but for neither the first nor last time we’ll note that Arsenal will quite correctly care not one jot about how much fun it is for the rest of us to watch them play football. They’re going to end the season as champions again; grudgingly we must concede this is the real quiz.

3. The manner in which Arsenal changed the pattern of the match in the second half is huge credit to Mikel Arteta and his players. The fact he was so visibly annoyed in the first half told you that the game was a thoroughly entertaining spectacle for the neutral but a maddening one for him.

He wasn’t about to let a second 45 minutes pass in that fashion. Arsenal first reintroduced the concept of midfield, and then set about thoroughly dominating it, chiefly through the endeavour and industry and class of Declan Rice.

4. It says a lot about Rice that he, a midfielder, was still Arsenal’s best player in that first half where the whole idea of midfield became almost an entirely theoretical concept. We’ve not actually checked the numbers, but if you told us the first-half action areas broke down as 70-1-29 we’d have no trouble believing it.

In that absurdly stretched and fun first half it simply became a game of two attacks against two defences. Rice made it his business to be the most important feature of both Arsenal’s elements in that equation.

Then in the second half, as Arsenal wrestled back control over the style of game it would be, Rice was even more impressive when given the chance to operate in more orthodox fashion.

He laid on the assist for the only goal of the game – one of two key passes he completed – and had more touches than any other Arsenal outfield player. Nobody in the game had more shots, and he also found time to complete three tackles, two clearances and an interception.

Rice wasn’t the only reason Arsenal won at Anfield in the Premier League for the first time since 2014, but his was a bigger part than any other individual’s.

5. Liverpool will kick themselves, though. Not so much over the frustrating but understandable way in which they were Arsenaled into submission in the second half, but for the careless way they frittered away all the good work they put in at both ends of the pitch in the first.

Arsenal’s goal was entirely avoidable, and Liverpool’s failure to find a decisive response almost entirely their own doing.

6. Let’s start with the goal, one that sadly for Liverpool falls into ‘catalogue of errors’ territory. It’s never a good catalogue, and doubly so against a team as ruthless and efficient as this Arsenal side are when handed a gift of this nature.

Alisson’s pass out to Jeremy Jacquet was clumsy and underhit. Jacquet, who was otherwise enormously impressive again, still shouldn’t have made quite the mess of it that he contrived to allow Arsenal to regain possession high up the pitch.

Yet even from here, with Arsenal swift and decisive in moving the ball out to Declan Rice to square for Kai Havertz to tap in, Liverpool failed to cover themselves in glory.

Virgil van Dijk was the most conspicuous of the Liverpool defenders reduced to the status of training cones as they watched Rice’s cross find its target. In a game that was always likely to involve fine margins, it was a ludicrously generous act from the hosts to make the opening goal so straightforward.

7. To emphasise those fine margins, of the last nine Premier League games between this pair, five have ended all-square, and three have now been won by a single goal. The only exception is a 3-1 Arsenal win at the Emirates in February 2004 when Leandro Trossard scored the third in added time after the visitors were reduced to 10 men.

There are few fixtures where it’s advisable to so casually donate your opponent a goal, but few where it is specifically inadvisable as this one.

8. What was hugely impressive in almost every way was how Liverpool responded to that massive setback. For the rest of the first half they set about Arsenal with industry and elan.

But that ‘almost’ is vital. For all Liverpool’s dominance in this period, for all that the game seemed to suddenly contain no midfield at all, a familiar Liverpool problem emerged.

A header sent wastefully over the bar by Alexis Mac Allister from Bradley Barcola’s cross was the only big chance Liverpool created. It is only the seventh big chance they have created all season, putting them 19th in that particular table.

It was also Liverpool’s 19th cross of a gloriously chaotic, magnificently un-Arsenal first half. They put in five crosses during the whole game against Brighton last week.

9. And yet at the end of that chaotic half of football, one Liverpool largely dominated and in which they dragged Arsenal kicking and screaming into the style of game they are desperate to avoid, David Raya had not made a single save. That would remain the case when the final whistle came.

Liverpool have quickly become really quite adept Iraolaball chaos merchants, but unless and until that starts to equate to clearer chances and cooler heads when said chances do arrive, they will remain limited in how far it can take them.

10. Liverpool will point with some justification to one specific incident that could have changed everything, mind. The failure of VAR to award Alexander Isak a penalty when his shirt was almost pulled from his back by Jurrien Timber was as inexplicable as Isak’s unnaturally calm reaction.

The whole incident had us feeling like we were taking crazy pills. Without Timber’s intervention, Isak has a clear header on goal from seven yards. Yet his response was to have a little joke with Timber about it. Admirable, in a way. But also absolutely maddening.

It’s hard to imagine he wouldn’t have got the penalty – whether on-field or via VAR – had he kicked up more of a fuss, which is what we suspect 99 per cent of professional players would have done in that situation.

And to be clear, we’re not even saying here he should have overreacted. Just the regular level of reaction to being yanked backwards when seemingly about to score would have sufficed. Nothing Oscar-worthy, just regular levels of irritation and arm-waving annoyance would’ve been sufficient.

But it’s also worth noting that not even that should have been necessary. It might explain why the on-field official was thrown off the scent, but there really is absolutely no excuse for VAR to have watched it back and still concluded there was nothing untoward.

It was the platonic ideal of a That’s What VAR Is For moment. And a crucial moment, in a crucial game. The lack of fuss and an unhelpful angle are enough to explain the original on-field decision. But what exactly were the VAR lads watching?

11. It was not the only curious refereeing decision in the first quarter of the game.

Trey Nyoni was astonishingly fortunate to get through the first 10 minutes of his first Premier League start without at least one yellow card. He could easily have had two.

Perhaps you could argue there was a veteran’s nous in the way he chose to introduce himself to the game by raking his studs down Martin Odegaard’s Achilles after a mere 55 seconds had elapsed, a stage so early in occasions such as this that we all know yellow cards are verboten lest the game descend rapidly into a farcical haze of yellow.

His second go, on Kai Havertz, was not quite so egregious but surely at the very, very least warranted a bit of totting-up card-waving.

There was also a genuinely baffling moment when a Bruno Guimaraes effort took a massive and obvious deflection off Virgil van Dijk that sent it spinning behind in the way only a deflection can, only for goal-kick to be the verdict.

12. After Nyoni’s second Achilles-raker, we knew for sure we were in for an all-timer from Gary Neville as he set a new personal best for earliest non-Romero declaration that a player had been “a lucky boy”. He’d already made a Neville Noise about a tight offside call against Havertz, who had only narrowly strayed beyond a disarmingly disjointed and uneven Liverpool defensive line that kind of fluked it.

Neville had been sparked into life by an early bit of Gabriel nonsense, the Arsenal defender and sh*thouse-in-chief rolling around the pitch within the first three minutes after pretending so egregiously to have been struck in the face rather than chest that if Rivaldo himself were watching he might be minded to think it was a bit much.

‘Embarrassing’ was the verdict from Neville. He has undeniably become a little bit of a caricature of himself as the years in the commentary box mount. It’s a fate that’s desperately difficult to avoid. But there remain two Neville-isms where his absolute elite levels remain unmatched an undoubted. When declaring someone or something ‘embarrassing’, and when watching the replay of a naughty challenge and announcing ‘He’s in trouble here, Romero/Martinez/Whoever’.

13. Luckily for all our collective sanity, Neville was handed a second-half opportunity to declare a Liverpool player ‘embarrassing’ in equally withering fashion to head off accusations of bias and – in the ludicrous world in which we all now reside – perhaps even lawsuits, who knows.

Alexis Mac Allister was the second target of his ire, and rightly so after getting wound up by Odegaard and then pretty blatantly trying to get Noni Madueke sent off by pretending to have been headbutted.

VAR may have been asleep at the wheel in the first half, but came close to matching Neville levels of withering dismissiveness with their assessment here: ‘There is some contact as Madueke and Mac Allister square-up. In my opinion, it’s not forceful, not violent, not brutal.’

14. Florian Wirtz remains a frustrating curiosity of a player. He had three attempts at goal, none of them on target (although one did thump against David Raya’s crossbar) and created no chances for team-mates.

Even when offering what was on the surface quite an encouraging display, he still just doesn’t do enough for what Liverpool have invested in him, and still makes wrong decisions on a maddeningly frequent basis when presented with encouraging situations where there is a pretty obvious best option. We have a suspicion he might be extremely irritating to play with.

15. Everyone in a Liverpool shirt was a little bit Wirtz in the second half, one in which not even the famed ability of The Kop to suck the ball goalwards could have any effect given how infrequently the ball came within any kind of threatening range.

After the blood and thunder of the first half, it was if anything Arsenal who looked more likely to add to their advantage after the break, coming closest when Christos Tzolis – lively on his return to the side – drew a fine fingertip save from Alisson that grabbed the attention in large part because it was so rare an occasion to see either goalkeeper pressed into serious action.

16. The overriding feeling at the end of an always-absorbing and occasionally unexpectedly thrilling game of football was that Arsenal are overwhelmingly likely to retain their Premier League title. And it really would be best for everyone if they can do so by accumulating more points than everyone else.

A large part of us would very much like to see the end of the season arrive with absolutely no certainty about who the champions actually are, but that’s just because we’re pricks. There’s no pretending that it’s a desirable outcome, even if it’s a funny one.

Arsenal here showed us two ways they can win the title and that’s encouraging. The free-flowing, high-pressing and dare we say it entertaining team that ran Liverpool ragged and opened up a lead they would never surrender in the first quarter of an hour or so. Then we saw the familiar controlled defensive machine in the second half.

The 30 minutes in between is where some hope can be found for anyone else. It was undeniably striking to see that control ceded in the way that it was. But there are few teams who are capable of pulling that off. And even here it didn’t even work. Arsenal are going to take some stopping and we’re really not sure where, over this specific 38-game season, the meaningful challenge can be found.