The Gunners were the favourites to progress to the last eight of the competition after the draw was made but everything went wrong for them in the first leg in France.
Substitute Alex Iwobi rifled wide from the edge of the penalty area as Arsenal tried to settle the tie before Aubameyang came up with what proved the decisive goal in the 72nd minute.
Gunners fans are well aware of that fact, with many commenting on his form in recent times, as well as his excellent performance against the French outfit, when reacting to the win on social media after the full time whistle.
Aubameyang opened Arsenal's scoring with a goal just five minutes in, while Ainsley Maitland-Niles made it 2-0 with a score of his own of an Aubameyang assist in the 15th minute.
However, Rennes will consider themselves hard done by in defeat. Following Maitland-Niles' goal, Arsenal were shaky at times, mostly due to the erratic defending of Shkodran Mustafi, as usual.
Aubameyang clearly picked up the ball in an offside position and his cross was put into the net by Maitland-Niles.
The first leg is set to take place at the Emirates on April 11, and Kolasinac has insisted that the Gunners must avoid another damaging defeat.
He has reason to complain, though.
Petr Cech, in what could have been the Czech great's last game before retiring at the end of the season had Arsenal not progressed, turned M'Baye Niang's shot from outside the area onto the post.
"The most important is that we won and everybody is happy and proud".
"It was hard for us because we had to play with 10 men for about 50 minutes of that first game as well".
"I think today we played very consistently over 90 minutes, being competitive without the ball and very serious defensively".
"Today, Inter (Milan) are out, Sevilla are out - a big surprise".
"This comeback was very hard, but I think the reaction was very good from every player", Emery told reporters.
"Playing under pressure is good. The second goal changed things enormously, even if they were better than us and deserved to qualify".
The ill-tempered feel to the match continued throughout a nervy second half as a number of strong challenges went unpunished.