The striker put Arsenal ahead within four minutes, firing in Aaron Ramsey’s cut-back, before setting up Ainsley Maitland-Niles before half-time at Emirates Stadium.
He then poked in Sead Kolasinac’s low cross after the break to make it 3-0.
Arsenal will be in the draw for the quarter-finals on Friday at 12:00 GMT.
They join fellow English side Chelsea in the last eight after they thrashed Dynamo Kiev 8-0 on aggregate.
It is the second successive season Arsenal have made it through to the last eight – they were knocked out in the semi-finals last year following a 2-1 aggregate defeat by Atletico Madrid.
Aubameyang shines for Gunners
Despite trailing 3-1 from the first leg and needing to score at least twice, Arsenal remained favourites to progress to the quarter-finals and they got off to a brilliant start.
Alexandre Lacazette, who was eligible to play after a ban was reduced, had a great chance after just three minutes when he latched onto Ramsey’s ball over the top, only to be denied by Rennes keeper Tomas Koubek.
Aubameyang was energetic, efficient and dangerous throughout and it was his willingness to chase the ball down which led to the second goal.
There was some fortune as he appeared to be offside when Ramsey’s threaded pass was kept in on the byeline but with no video assistant referee, Maitland-Niles finished off the move with a thumping header in the centre.
He celebrated by throwing on a Black Panther mask which had been stored behind the goal – the latest in his trademark superhero celebrations.
Only Manchester City’s Sergio Aguero (18) has scored more goals than Aubameyang (17) in the Premier League and the Arsenal forward has now picked up four goals and two assists in seven Europa League games this season.