How Arsenal forward Alexis Sanchez tore West Ham apart and what Arsene Wenger's side must do to launch genuine title challenge

Well, Carroll got his goal, but it proved utterly inconsequential, and for that Arsenal have Sánchez alone to thank. So step forward Sánchez, shrugging off Arthur Masuaku like an itchy panto outfit and scoring a delightful solo goal. Again Sánchez, finishing crisply first-time from 18 yards. And for his party trick, Sánchez once more, running onto Alex Oxlade-Chamberlain’s long ball, sending goalkeeper Darren Randolph for a Fanta, and chipping with an impudence that makes opposition defenders want to slap him.

There are points in a season when it falls to one player to seize the game by the scruff of the neck. Özil, for all his undoubted qualities, is rarely that man. Titles are won by many things: a settled defence, options off the bench, not being Liverpool. But you also need a slug of individual brilliance, and on what threatened to be a fairly grim evening, Sánchez delivered.

Let’s not get carried away here. We’re not saying Sánchez will win Arsenal the title. But what’s becoming increasingly clear is that they haven’t got a hope without him.

How did Gabriel do at right-back?

Wenger admitted before the game that Gabriel had been picked partly for his height, and although there were times when he looked unmistakably like a converted centre-back, the threatened Payet-geddon down the West Ham left never materialised. Nacho Monreal offered more going forward, but Gabriel was largely sound at the back, apart from one instance when he let Manuel Lanzini drift behind him for West Ham’s best chance.

Certainly, Gabriel will reflect that Héctor Bellerín makes the job look a lot easier than it is. He was injured just before half time fending off a goal threat at the back post, and earned another thwack in the head while leaping with Arthur Masuaku. A perfectly decent stop-gap, then, but about as viable a long-term option as Wenger himself.

Did Carroll soar through the skies like a vengeful albatross made of pure fire and make everyone’s dreams come true?

The fans were singing his name before he even came on. As he prepared to make his entrance, assistant coach Nikola Jurcevic was giving him some last-minute instructions from a tactical dossier. There was something in Andy Carroll’s bloodthirsty expression that suggested he may not have been giving Jurcevic his full attention. His first touch came after a couple of minutes, a diagonal ball from Lanzini. Carroll made three attempts to control the ball, and somehow managed to put it out of play with two of them.

But then, seven minutes from time, Payet’s free-kick crashed off the bar and rebounded away from goal, straight towards Carroll’s head. In that fraction of a second an immense calm seemed to settle over him, a calm that said: “Don’t worry, lads. I’ve got this”. It may not have been the best night to be a West Ham fan. But the big man’s back. And that’s something, at least.

Who was the man of the match?

Sanchez, obviously. But an honourable mention for Laurent Koscielny, who for long periods offered the poise and maturity that Arsenal have so often lacked. Won his battles, covered the ground well and made one excellent last-ditch intervention to cut out a Lanzini cross.

What do both sides need to work on in the week?

West Ham United: Oh god, everything. Defensive positioning, first touch, second balls. But with a trip to Anfield coming up, they would probably settle for some good news on the injury front, with Aaron Cresswell, Michail Antonio and Cheick Kouyate all missing here.

Arsenal: Killer instinct. And if that sounds strange after a 5-1 victory, then remember that much better teams will punish Arsenal for not finishing the game off in the first hour. Sánchez isn’t going to bail them out with a hat-trick every week. Probably. We’re almost certain.