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 Thursday.
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.
What does it mean? Champions League dreams alive for Gunners
It would need an extraordinary turn of events for Arsenal to pip north London rivals Tottenham to the last Champions League qualification place by finishing in the Premier League's top four. However, Emery now has a great opportunity to lead Arsenal back to Europe's elite as the winners of the Europa League will be granted a qualification spot in next season's Champions League.
Alert Aubameyang saves Arsenal twice
Before Aubameyang struck his first goal, Arsenal were enduring their most nervous moments of the tie. But the Gabon international is made for the big occasion and he quietened the usually raucous Mestalla crowd before later silencing them completely. Aubameyang, who also scored Arsenal's late third in the opening leg, stamped his name all over the tie.
Ozil a passenger on Europa League journey
This was the sort of occasion Mesut Ozil ought to decorate with his undoubted ability, but the former Germany international showed nothing of his precious playmaking gifts. Given a rough ride by home fans, shushing them as he was substituted early was his only notable contribution.
Key Opta Facts
- Arsenal have qualified for their seventh European final (1 Fairs Cup, 3 Cup Winners' Cup, 1 Champions League, 2 UEFA Cup/Europa League), but lifted the trophy on just two of the previous six occasions.
- Valencia lost for just the second time in their last 22 home games in all competitions (W15 D5).
- Arsenal registered a win away to Spanish opposition for the first time in eight games (D2 L5), since a 1-0 win at Real Madrid in February 2006.
- Including finals, Arsenal manager Emery has won his last 19 Europa League knockout ties, last being eliminated from the competition in the 2011-12 semi-finals with Valencia.
- Valencia's Gameiro has been directly involved in 12 goals in his last 12 starts in home Europa League games, scoring 11 and assisting one.
- Aubameyang has netted 29 goals in all competitions this season, a haul only Sergio Aguero (31) can better among Premier League players.
- Since his Arsenal debut in August 2017, Lacazette has been directly involved in 51 goals for the club in all competitions, more than any other player (36 goals, 15 assists).
- Excluding own goals, 11 of Arsenal’s last 12 Europa League goals have seen Lacazette and Aubameyang involved (four goals and one assist for Lacazette, and six goals and two assists for Aubameyang).
Arsenal wrap up their Premier League campaign away to Burnley on Sunday, needing a win, as well as a Tottenham defeat at home to Everton and a large goal difference swing to qualify for the Champions League. Valencia, also fighting for a top-four berth in LaLiga, host Deportivo Alaves on the same day.