The Gunners have endured a difficult start to the Premier League campaign, losing to Brentford and Chelsea in succession and increasing pressure on Mikel Arteta.
But the Arsenal manager was rewarded for naming a strong XI at the Hawthorns, where West Brom changed its entire line-up.
Aubameyang scored twice and created a third for Nicolas Pepe in the first half, then completed his treble in style either side of strikes from Bukayo Saka and Alexandre Lacazette after the restart.
West Brom enjoyed flurries early in either half but were largely on the back foot and trailed when Saka's shot was spilled at the feet of Aubameyang.
Martin Odegaard then hit the post from a tight angle, but Aubameyang was on hand again when Arsenal next hit the woodwork, profiting on the rebound from Pepe's attempt.
Aubameyang turned provider for Pepe when Alex Palmer blocked his route to goal, before Saka added a popular fourth from Odegaard's flick.
A glorious curling effort from Aubameyang found the top-right corner to cap a fine individual outing, and Arteta introduced Lacazette to get in on the act, arrowing in a cutback from Pepe, who had moments earlier chipped against the crossbar.