Maribor took the lead through Milivoje Novakovic in the 83rd minute of action, but Jonathan Hayes levelled the scores two minutes from time to leave the tie delicately poised ahead of the return match in Slovenia next week.
The Scottish outfit made a fast start on home soil and had three half-chances inside the first four minutes, but Jayden Stockley failed to connect on two dangerous crosses, before Niall McGinn went close with a volley.
Maribor had a golden chance of their own in the 17th minute when Marwan Kabha found himself unmarked inside the home side's box, but the midfielder fired over the crossbar from 10 yards out.
Hayes came close to sending Aberdeen ahead just past the hour after firing one towards the bottom corner, but his effort just missed the post, before Kenny McLean fired high and wide 15 minutes from time.
Aberdeen did have the ball in the back of the net in the 80th minute when Rooney converted after smart work from McGinn, only for the linesman to wave his flag and rule it out.
It went from bad to worse for the home side three minutes later when Novakovic drilled a long-range effort past Joe Lewis to hand Maribor an advantage, but Aberdeen levelled in the 88th minute when Hayes found the back of the net after smart work from Rooney.