Until Theo Walcott nodded in Nacho Monreal's cross in the 53rd minute, it seemed Arsenal's November troubles -- Wenger's team have a history of performing poorly during this calendar month -- might catch them out again.
Indeed, even after that, there was a further element of fortune to Arsenal's victory, as Bournemouth were denied a second penalty when Monreal very clearly committed a 73rd-minute handball from Simon Francis' attempted cross.
When Sanchez opened the scoring in the 12th minute after seizing on a terrible back pass by Bournemouth defender Steve Cook, an afternoon of plain sailing for Arsenal seemed most likely. But then came a revival from the visitors and decision-making by referee Mike Jones that had the Emirates boiling in rage.
First, he denied a penalty when Nathan Ake looked to trip Sanchez, before giving one at the other end in the 23rd minute. If anything, it looked as if Callum Wilson had fouled Monreal, rather than the other way around, but Jones pointed to the spot and Wilson took the kick himself, scoring coolly.
The first half was thrilling, end-to-end stuff. Entertainment levels were perhaps enhanced by some low-quality defending, but the attacking level was definitely high. Bournemouth had little answer to Sanchez other than to make repeated fouls on the Chilean powerhouse.
The same was true for Arsenal with Wilson, who gave an exemplary centre-forward display until he was substituted in the 63rd minute and especially in a spell following the equaliser as Bournemouth had Arsenal rocking on their heels. It was the visitor, rather than Wenger's team, playing inventive, flowing football.
Arsenal continued to miss the playmaking qualities of Santi Cazorla, whose return date from an Achilles problem appears some time off. Granit Xhaka and Mohamed Elneny as a pairing could not replicate the Spaniard's genius or "technical stability," as Wenger termed it this week.
Mesut Ozil was also having one of his disappearing days. It was left to the irrepressible Sanchez to provide the inspiration, and he closed the first half by crashing the ball off the crossbar with a venomous angled shot.
He powered Arsenal's second-half improvement, which saw them dominate possession and territory, though more of his colleagues also came to the party; Walcott, Ozil and Alex Oxlade-Chamberlain all found more space. PLACE YOUR CONTENTS ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Click Here To Download A Free Guide That Shows How To Make 100k Weekly Without Lifting Your Finger (Using An Autopilot System) Click Here To Discover Why Experts Conclude This Money Making Secret Is 100% Legal, 446.67% Better and 217% Safer Than MMM.