The satisfaction of a straightforward victory was, for Arsenal, topped by a moment that may have lasting significance. Kai Havertz has been subjected to intense scrutiny since moving from Chelsea, struggling to find his groove even if opprobrium has been premature in the extreme. A run of respectable all-round showings needed some end product and it came when, handed the chance to see off Bournemouth’s perfunctory challenge, he comfortably beat Neto from the spot. The away support had cheered when he took the ball; they could hail his first goal for the club within moments and Arsenal’s players, led by Gabriel Magalhães, made sure Havertz soaked up the acclaim.

Bukayo Saka and, with another penalty, Martin Ødegaard had already put Arsenal comfortably ahead. Ben White completed the rout with a header in added time and the win breathed life into their efforts to keep pace with Manchester City. It also meant the anticipated battle of wits between Mikel Arteta and Andoni Iraola, boyhood teammates at the San Sebastian club Antiguoko, was settled before it could ever catch light. Bournemouth dropped into the bottom three with this result and, while they can point to a softer-looking October after a tough start, need to become tougher in both boxes sooner rather than later.

Saka has ticked most boxes for Arsenal over the past five years and this time showed a poacher’s instinct in putting them ahead. The opening stages had been low-key but, when Gabriel Jesus peeled away and met Ødegaard’s cross near the left byline, Bournemouth were exposed. Jesus was probably trying to head the ball across goal but saw it glance off the post; Saka, perfectly located in the six-yard box, was never going to miss and stooped to convert the rebound.

It was the start Arteta had demanded. His pre-match smoke and mirrors had brought concerns Saka, Declan Rice and William Saliba would miss out but there was little surprise when all three showed up. None of them are easily replaceable and Saliba proved the point 12 minutes in when, with Dominic Solanke poised to take a crack at David Raya’s goal, he showed speed and immaculate timing to intervene. Such is Saliba’s assurance that he managed to play the ball back off Solanke for a goal kick.

Seconds previously Havertz had seen an angle shot deflected into the side netting but, those glimmers apart, neither side had done much to raise pulses. Once behind, though, there was a sense Bournemouth would be bereft if they conceded again. Oleksandr Zinchenko, frequently adding to the midfield numbers with grace, swiftly took aim from 25 yards in an attempt to settle things early but saw Neto bat his drive away.

The next time Zinchenko exerted an influence infield, Arsenal would go one better. They had not been entirely dominant since scoring but Bournemouth, for all their willingness to attack their flanks and probe around the 18-yard line, had failed to create a meaningful chance. The interval was nearing when Eddie Nketiah passed inside to Zinchenko and sprinted down the left channel, running beyond Illia Zabarnyi and taking the perfectly-weighted return. Max Aarons had to ensure his challenge was flawless upon choosing to dive in but was clumsy and late, Nketiah getting toe on ball to win a clear penalty. Ødegaard converted calmly and, while Gabriel had to deny Philip Billing immediately at the other end, Arsenal now had overwhelming control.

Aarons had not covered himself in glory but, six minutes into the second half, Ryan Christie outdid him with the most ungainly of lunges on Ødegaard. Arsenal had been pressing for a third when, after a Saka cross had been half-cleared, Ødegaard took possession 15 yards out. He was facing away from goal, posing minimal direct threat, when Christie steamed in; Saka stood over the penalty but left it for Havertz, who did the rest and wrote the day’s feelgood story.

Saka was also behind the only note of concern for Arteta. He takes weekly buffetings but looked in clear pain when limping off 14 minutes from time. City await next Sunday and, with the stakes freshly raised, Arsenal need their talisman to dust himself off again.