In a dramatic end, Dortmund netted twice in two minutes to overpower the Spaniards who thought they may have been through with only a minute or so remaining in the return bout.
Joaquin had Malaga ahead in the 25th minute following the scoreless first leg when he tucked home Isco's pass into the back of the net, just past the inside of the post.
Both sides had opportunities to go ahead early in the second half and it eventually it was Malaga who took the advantage with eight minutes of regular time left when Isco and Julio Baptista combined to play in Eliseu who slotted home past Roman Weidenfeller.
Just as it seemed like there was an upset on the cards, Dortmund flexed their muscle with Reus drawing them level (but behind on away goals) with a simple finish in the 91st minute before Felipe Santana was on hand at the back post on the goal-line to fire home Julian Schieber's miscued effort and the Germans into the final four in theatrical fashion.
2012/13 UEFA Champions League - quarter-final second leg
Signal-Iduna Park, Dortmund - 65,829