In the absence of the want-away Chilean, Arsene Wenger's men did not have a saviour at Dean Court
Defeat at Bournemouth showed how likely Arsenal are to miss Alexis Sanchez
Things will look better for Arsenal at some stage in the coming weeks.
It is because the one asset Arsene Wenger had always had is the capacity to arrest a dismal run just as it lurches into full crisis.
But this is a very gloomy new year for the manager so far. His unprecedented third-round elimination from the FA Cup has now been followed by a first ever defeat by Bournemouth - 2-1 after the Londoners had held the lead.
Arsenal are in all likelihood about to lose their starriest footballer, too.
At the offices of the club, the club’s executives have wearily been valuing Alexis Sanchez, putting an ample price on a player who is itching to leave the club and will only do so with retail potential only for this month, with his contract expiring in June.
Sanchez, who has been informed in detail of interest from Manchester City and United, did not travel to the south coast on Sunday.
In his absence his value grew: Arsenal were rickety without him. Of course, whether Sanchez - who has had an ordinary season by his standards - would have elevated standards in a very ordinary Arsenal performance is speculative.
It would have been hard for him not to. The football was untidy for most of the opening first 45 minutes.
Jack Wilshere, back in Arsenal’s midfield regularly, provided pleasing moments of vision with his passing. But it was not until after the hour that there was edge-of-the-seat drama and composure in attack.
The better team for most of the opening half hour, Arsenal did hit the frame of Asmir Begovic’s goal, via a poised tee-up and then a rasping shot from Ainsley Maitland-Niles.
Bournemouth found their higher gear just before half time. A period of pressure yielded a menacing Ryan Fraser shot, blocked by Calum Chambers, and a hearty appeal for a penalty when Alex Iwobi cleared a corner with what looked like helpful use of the forearm or elbow.
Arsenal had sensed a structural weakness from early on in a Bournemouth defence which seldom keeps a clean sheet.
It was along the home side’s left flank, guarded by Charlie Daniels, who is a galloping sort of a wing-back when - as on Sunday - Bournemouth play with a back three. But he leaves space in his wake. When you can attack that with a player as fast as Hector Bellerin, you have an avenue worth exploring.
Arsenal probed that area, and when Iwobi released Bellerin, the Spanish speedster made his way quickly towards goal. Though Begovic partially blocked his effort, the shot swirled up, span and dropped over the goal-line.
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Bournemouth responded, some 20 largely comfortable minutes for Arsenal later, with a trick from the same tactical manual: a dart into the space behind the left wing-back, Maitland-Miles, and a goal.
The architect was the lively Fraser, whose drilled, pinpoint cross invited Callum Wilson to back his run against the advancing Petr Cech. Wilson won the race, and had the finish to exploit the chance.
“The fans were a bit flat so we needed to get them involved,” Wilson felt at the time of the equaliser. “It was a massive lift.”
The Bournemouth players felt it and Wenger, marooned in the grandstand stand because he was serving out the remainder of his touchline ban, watched his afternoon deteriorate suddenly and brutally.
Wilson received a high ball skilfully with his back to goal and laid a pass off to an unpoliced Jordon Ibe. Arsenal had been busted. Ibe’s first goal for Bournemouth squirmed through Cech’s attempted save.
The goal catapulted Bournemouth from the frontier of the relegation zone up to 13th. As for their guests, Arsenal flail in sixth place, six points behind Tottenham Hotspur, who themselves are struggling to grasp a top four spot.
And Sanchez’s days as Arsenal’s saviour and superstar are very nearly done.