Former Arsenal midfielder Arteta was in the dugout for the first time since being appointed Unai Emery's successor.
Having opted to recall Mesut Ozil to his starting line-up in one of three changes, Arteta saw his side fall behind to Dan Gosling's goal 10 minutes before half-time.
However, Aubameyang tucked in a second-half leveller to ensure Arteta gained a point in his debut as a manager.
Arsenal almost fell behind within five minutes as Bernd Leno's right foot denied Ryan Fraser after good work from Lewis Cook and Callum Wilson.
England international Wilson then fired a volley over following a one-two with Fraser as the Cherries continued to press down Arsenal's left.
It was from that flank that the opening goal arrived, an overlapping Jack Stacey sliding the ball across for Gosling to poke home a first-time finish at the near post.
The Gunners were fortunate not to be 2-0 behind at the break too, with Leno having to claw Joshua King's effort behind after the Norwegian had beaten two Arsenal defenders.
Aubameyang had been virtually anonymous in the first period but he fired over early in the second half and almost collected a brilliant threaded pass from Ozil.
However, in the 63rd minute, the striker was in the right place to sweep home after Reiss Nelson's shot deflected into his path.
Alexandre Lacazette, another of those brought into the XI by Arteta, then bore down on goal following a David Luiz throughball but Chris Mepham's fine last-ditch intervention forced a corner.
Bournemouth thought they had a winner nine minutes from time when Callum Wilson turned home after Leno had spilled Harry Wilson's shot into his path.
Yet the flag was correctly raised for offside against the Bournemouth forward, meaning Arteta avoided a losing start.