Sitting in 11th on the Premier League table, the Gunners need to win the Europa League to guarantee themselves continental football next season.
Diogo Goncalves levelled for Benfica just before the break with a superb free-kick.
And the visitors - although the game was played at the Karaiskakis Stadium in Greece because of Covid-19 restrictions - took the lead on the 61st minute mark through Rafa Silva.
Aubameyang was criticised for missing a number of chances in the first leg, but the Gabon international atoned with his second of the night.
Another superb cross from Saka was met at the back post by Aubameyang, who nodded a simple header past Benfica goalkeeper Helton Leite.
Aubameyang told BT Sport: "I think everyone is happy tonight.
"Definitely I had this in my head but this is what gives me power every day to take the errors from the past and transform it to strength"
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