Arsenal will face Villarreal or Valencia in the last four if they can get past Napoli, with the first leg switched to the Emirates to avoid two ties being played in London on the same night.
With the Ligue 1 side leading 3-1 from the first leg, Aubameyang and Ainsley Maitland-Niles scored in the first 15 minutes of Thursday's return to draw Arsenal level on aggregate.
But they put in a commanding performance as they won 3-0.
However, Rennes will consider themselves hard done by in defeat.
However, it was not forthcoming and with VAR not in operation in the Europa League unlike the more lucrative Champions League, Maitland-Niles's downward header from Aubameyang's cross was allowed to stand. "The offside was very clear, you don't need VAR to see it".
The smoke had barely died down from the red flares the Rennes fans let off in the away end before the home side had pulled the aggregate score back to 2-3 with practically the whole game to play.
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Arsenal needed two goals, at least, and started without Sokratis Papastathopoulos in defence after last week's red card.
Arsenal have overcome Manchester United and Rennes in quick succession, and the striker has been a key man in both matches. "And the last teams, they are all very important, and it's going to be very hard", Emery said. "Today, Sevilla are out, Inter are out".
"This comeback was very hard, but I think the reaction was very good from every player", Emery told reporters.
And he says not many people would have thought that at the beginning of the campaign. "The second goal changed things enormously, even if they were better than us and deserved to qualify".
"But I think we can feel this competition like in the Premier League, to do a good way and create, with our supporters, a big atmosphere and a big feeling together to do this way in the Premier League and also here in the Europa League".