Arsenal’s 3-1 victory against Bournemouth perfectly summarised their recent performances: three shots on target and three goals. It means their total for November, traditionally the month where Arsène Wenger’s side endure a slump in form, is 10 goals from just 11 shots on target – an entirely unsustainable rate.

In a flat performance, Arsenal’s standout performer was Alexis Sánchez. Reverting to his centre-forward role having played wide in the 2-2 draw with Paris Saint-Germain, the Chilean demonstrated his all-round ability here, scoring two goals, hitting the bar with a powerful shot from a tight angle, and also creating five chances for his team-mates, the most of any player on the pitch. He was Arsenal’s chief provider, and most dangerous goal threat.

In last weekend’s 1-1 draw at Manchester United, Sánchez was guilty of dropping too deep, but here he varied his position intelligently without abandoning his centre-forward role entirely. When he did move towards play, Theo Walcott drifted inside to become a temporary centre-forward, and Mesut Özil made sporadic runs in behind too. There were signs that Sánchez and Özil are becoming a proper partnership, combining regularly in counterattacking situations.

From the moment Steve Cook was cautioned for a clumsy late foul on Sánchez in the right-back zone, inside five minutes, it seemed the Bournemouth defender was set for a tricky afternoon. Sure enough, Sánchez’s opener came when he exploited a woefully underhit Cook backpass before converting easily. It felt somewhat similar to his opener in the 3-0 victory over Chelsea in September – his only previous goal at the Emirates this season – when he exploited Gary Cahill’s sloppiness in possession. Cook’s mistake was entirely unforced, but Arsenal are nevertheless more likely to win the ball in advanced positions with Sánchez up front, always prowling dangerously in the hope of an error. He also tracks back when required – at one stage, with Bournemouth building play in central midfield and Özil seemingly not interested in regaining possession, Sánchez sprinted back 30 yards, won the ball, and Arsenal were on the attack again.

This was not a flawless individual performance: it was Sánchez who conceded possession shortly before Bournemouth were awarded a penalty, when Nacho Monreal was adjudged to have fouled Callum Wilson. A more natural centre-forward might have held up the ball, and while Sánchez is surprisingly strong for a man of his size, playing with his back to goal remains his major weakness as a centre-forward.

Nevertheless, he repeatedly drove Arsenal forward, lifting the tempo when the Emirates was quiet at 1-1, and later gestured for Arsenal to calm the game and retain possession reliably after they’d taken the lead. For such a frantic, high-tempo player, Sánchez is also intelligent in a tactical sense and capable of altering his style to suit the nature of the game. He was also seen commanding his team-mates against PSG, and is arguably Arsenal’s most natural leader.

His best contributions came when Arsenal were 2-1 ahead, after Walcott headed home from Monreal’s cross. That meant Bournemouth pushed men forward and Arsenal had space to break into. When attacking into the inside-left channel Sánchez nearly found Özil with a delicate pass after the German had shown fantastic movement to drift towards the far post before suddenly producing a lightning near-post run, and the Chilean played the game’s best pass with a truly outrageous outside-of-the-boot ball in behind, which Özil should probably have made more of.

It was only fitting that Sánchez wrapped up the scoring, a tap-in after good work from Olivier Giroud, who was introduced as a substitute, down the right. Giroud will feel his constant contributions from the bench merit a permanent place in the side, but realistically Wenger will consider this evidence Giroud is a fantastic plan B. Sánchez is now his main man up front, and, in this mood, as dangerous as any footballer in the Premier League.