The victory caps a fine week for English sides in Europe, with all six Premier League teams competing in continental competition progressing through to the quarter-finals.
Needing to score at least twice to progress, Unai Emery named a strong side, showing just two changes from the team that beat Manchester United at the weekend.
That included a recall for Alexandre Lacazette, who was cleared to play after his three-match ban was reduced to two by UEFA earlier this week.
The Gunners made the perfect start, scoring twice in the opening 15 minutes to level the tie on aggregate and move ahead on away goals.
First, Maitland-Niles and Aaron Ramsey combined well down the right, with Ramsey crossing low for Aubameyang to score the opener from close range.
Ten minutes later, Aubameyang looked to be in an offside position when he ran onto Ramsey’s return pass inside the penalty area, but the flag stayed down and the Gabon striker lofted a teasing cross to the far post for Maitland-Niles to bury a downward header beyond Tomas Koubek.
Aubameyang had the chance to extend Arsenal’s advantage still further but his acrobatic bicycle kick from Mesut Ozil’s cross went well wide.
Ozil and Lacazette then combined well to tee up Ramsey on the edge of the area, but his effort was saved by Koubek.
Rennes offered little as an attacking threat in reply, with Hatem Ben Arfa firing a tame effort into the hands of Petr Cech shortly before half-time.
The French side had a glorious chance to get back into the game at the start of the second half when Clement Grenier dispossessed Shkodran Mustafi and teed up M'Baye Niang, but his effort from the edge of the box thumped off the post.
Rennes began to grow in confidence as the second half wore on, with Ismaila Sarr seeing an effort well blocked by Sead Kolasinac before Ramy Bensebaini struck the post with a first-time volley, though the offside flag had gone up.
But, just as the visitors looked to commit more men forward, Arsenal grabbed their third.
Substitute Henrikh Mkhitaryan fed Kolasinac down the left and his fizzing first-time cross was converted by Aubameyang for this second goal of the evening.
Aubameyang could have grabbed his hat-trick a few minutes later but skewed the ball wide from Ramsey’s pass.
However, that miss mattered little as the Gunners comfortably saw the game out to secure their place in the hat for tomorrow's quarter-final draw.