Kevin Gameiro's early opener cut the deficit for Valencia, beaten 3-1 last week, but Aubameyang swiftly hit back for the Gunners at Mestalla on Friday (NZST).
And when Alexandre Lacazette, who scored twice in the first leg, put Arsenal ahead, their place in the Baku final later this month was seemingly secure, despite this week's European drama.
Gameiro struck again but Aubameyang killed the tie off with a second goal of his own and Arsenal head coach Unai Emery, a three-time winner of the competition with Sevilla, will now have a chance to add a fourth title after downing former club Valencia.
Valencia took the lead in the first leg and Marcelino's men did so again in the return, with Gameiro on target in the 11th minute.
Ainsley Maitland-Niles had a shot saved by Neto at the other end but Valencia broke rapidly, with Gameiro turning home Rodrigo Moreno's low left-wing cross.
Arsenal swiftly levelled the second leg, though, as Valencia failed to deal with a Petr Cech long ball and Lacazette flicked on for Aubameyang to brilliantly smash past Neto.
Dani Parejo bent a free-kick wide of Cech's left-hand post then Lacazette should have struck in the 39th minute, clipping the outside of the post after brilliant Aubameyang play.
Lacazette made amends, though, collecting Lucas Torreira's pass, turning neatly into space and rifling across Neto to make it 5-2 on aggregate to the Gunners.
Gameiro's second of the game, which saw the striker bundle past Cech after inadvertently blocking an effort from Daniel Wass, reduced the arrears but Aubameyang had the final say.
Maitland-Niles brilliantly skipped clear on the right wing and Aubameyang got ahead of his man to turn home a near-post finish, before his 29th goal of the season in all competitions secured the match ball, with Valencia tempers spilling over at the full-time whistle.