Callum Wilson nicked in ahead of Petr Cech to score the equaliser in the 70th minute and four minutes later the stirker turned provider to set up Jordon Ibe for the victor.
Bournemouth, meanwhile, climb to 13th but remain just four points above the bottom three. We had to win the game. Get the app to get the game. "Those points lift us further away from the bottom three".
Desperate for a win, the visitors started brightly on the south coast with youngster Ainsley Maitland-Niles firing against the crossbar in the eighth minute.
Despite dictating much of the early possession Arsenal clearly missed their more illustrious attacking talents with Alexandre Lacazette cutting a lonely figure without the cutting edge of Sanchez and the injured Mesut Ozil.
Alex Iwobi tested home keeper Asmir Begovic before Bournemouth midfielder Dan Gosling was booked after going to ground under a Shkodran Mustafi challenge when the Arsenal player appeared to have caught him.
Bournemouth were perhaps quite unfortunate not to be awarded a penalty before the break as Iwobi looked to have moved his arm towards the ball from a corner.
It was Ibe's first league goal for Bournemouth.
Wilshere was anxious to make a good impression on his return to the club where he spent last season on loan while Arsenal were keen to register their first victory since the turn of the year.