Arsenal have felt the ghosts of Novembers past but this was a win to restore a measure of stability. It was not a vintage performance and there was a period in the first half after Bournemouth had equalised through Callum Wilson’s hotly contested penalty when the visitors appeared to be the likelier scorers of the next goal.

Arsène Wenger admitted there were nerves at that point and Arsenal would enjoy a let-off in the 72nd minute when Simon Francis’s flicked pass inside the area hit Nacho Monreal’s hand only for Mike Jones to ignore the appeal for another penalty. Eddie Howe, the Bournemouth manager, also felt that Jones had overlooked a claim for his team when Shkodran Mustafi shoved Steve Cook at a corner at the start of the second half.

Arsenal had the better of it overall and, inspired by Alexis Sánchez, they got the victory they needed to answer those of Chelsea, Liverpool and Manchester City from Saturday. Sánchez had put Arsenal in front early on and the Chilean added the gloss during stoppage time with a tap-in from the substitute Olivier Giroud’s pull-back following a slick counter. Sánchez now has 10 goals for the season and the only blot on his afternoon was the yellow card he received for an ugly tackle on Harry Arter. Laurent Koscielny had earlier escaped censure for what looked like a stamp on the Bournemouth midfielder.

Jack Wilshere’s struggle to find a role and rhythm eased by Howe’s alchemy | Barney Ronay Read more

Theo Walcott scored the decisive second goal – his ninth of the season – and it was a nice way for him to celebrate the birth of his second son, Arlo, who arrived on Friday, after Walcott’s wife, Mel, had gone into labour at 1.30am. It would last for 12 hours. Walcott was withdrawn on 75 minutes here and he sat on the bench with a heavy strapping on his lower leg, after taking what Wenger described as a minor kick. It was nothing on what Mel had endured.

Wenger also lost Mathieu Debuchy to a serious hamstring problem – the right-back lasted only 15 minutes of his first appearance for Arsenal since November last year – while Giroud, too, felt a hamstring problem that will need attention.

The three points were the balm to the pains and how they were needed. Arsenal had last won a November league fixture in 2014 and they came into this game on the back of three rather underwhelming draws in succession.

Bournemouth gifted Arsenal the opening goal when Cook attempted a back pass but found only Sánchez who, in yards of space, cut inside and shot low past the exposed Adam Federici. Arsenal dominated the first 20 minutes. Cook and Francis were booked after being beaten for pace by Sánchez and Alex Oxlade‑Chamberlain, respectively, while the excellent Nathan Aké made important blocks to deny Mesut Özil and Mohamed Elneny. Arsenal also shouted for a penalty when Aké caught Sánchez but the contact appeared to take place outside the area. Jones, who had a difficult afternoon, saw no foul.

Arsenal 3-1 Bournemouth: Premier League – as it happened! Read more

He did act – to the dismay of Wenger and the home crowd – when Wilson surged into the area in the 22nd minute. Across came Monreal, who flung out his arm and he caught the Bournemouth striker. The previous weekend, Wilson had been denied a clear penalty when Stoke City’s Ryan Shawcross cleaned him out but he was on the right side of this more debatable award. Wenger called it a “very soft one”. Mustafi was booked for his protests and Wilson, having dusted himself down, kept his cool to beat Petr Cech.

In a flash, the game turned. “We became nervous and the three [recent] draws played on our minds,” Wenger said. Adam Smith headed over on 26 minutes when gloriously placed, following Aké’s header back, and Brad Smith, playing his first league game for Bournemouth, worked Cech at his near post. Howe’s team played some neat football and the pace of Wilson, Josh King and Junior Stanislas worried Arsenal.

“The result was harsh on us – considering we gave them the first goal,” Howe said. “It was a penalty for handball [against Monreal]. The scoreline is difficult to swallow.”

Arsenal regained a foothold before the interval and it was Sánchez, inevitably, who was to the fore. He swiped over after an interchange with Özil and, on the stroke of half-time, he rattled the crossbar from an angle on the right.

Monreal was central to the goal that put Arsenal back in front and it was an excellent piece of technique with which he returned Özil’s cross from the right, which had flicked off Aké. The first-time ball was made to measure for Walcott, whose downwards header beat Federici. It was only the second time that Walcott had scored with his head in the Premier League.

Howe and his players were upset at Jones’s decision not to penalise Monreal for the apparent handball, while Cech saved at close quarters from the substitute and former Arsenal striker, Benik Afobe. The last word, though, would go to Sánchez.