Marco Reus and Felipe Santana both netted in stoppage time to take BVB from the brink of elimination and into the semi-finals of the Champions League
BVB failed to make their dominance count at La Roselada last week and it looked to be a recurring theme when Joaquin put Manuel Pellegrini's ahead but Robert Lewandowski equalised before the break. Eliseu looked to have broken BVB hearts with a late goal but two stoppage-time strikes courtesy of Marco Reus and Felipe Santana ensured an unbelievable comeback.
With the tie so delicately balanced from the first leg, such a conservative approach to the early stages from both teams was somewhat predictable.
As the minutes ticked by the hosts became more adventurous and in the 16th minute Lewandowski got his first chance to shoot at goal. He elected for an audacious 25-yard chip from Mario Gotze's pass but his overcooked attempt floated over the stranded Willy Caballero's goal.
Los Boquerones had struggled to string a meaningful attack together but in the 25th minute when they silenced the Signal Iduna Park.
Julio Baptista pounced on a poor clearance from Felipe Santana and his pass found Joaquin. After a tight give-and-go with Isco, the 31-year-old cut inside onto his left foot and sent a low shot past Roman Weidenfeller to net a huge away goal.
Apprehension and frustration began to spread around the stadium but their worries were eased five minutes before half time. Reus flicked Gotze's pass into the path of Lewandowski who rounded Willy and slotted the ball into the empty net to finish off a superb team move.
Joaquin was gifted a free header in the last action of the first half which Weidenfeller comfortably held and the start of the second half offered similarly enticing opportunities for both sides.
Lewandowski was unable to guide his shot past Willy after some more quick, crisp interplay with Gotze and minutes later the Weidenfeller managed to get a strong hand to the ball to keep Joaquin's header.
Malaga continued to squeeze the play and force the Bundesliga side into sending the long ball up from the back. However, when Sergio Sanchez failed to deal with one such pass Gotze could not find the from a glorious position in the 53rd minute.
The organisation of Pellegrini's defence was exemplary and after Dortmund had a goal ruled out correctly for offside, Duda's thunderous effort almost added to the disappointment of the home fans.
The heroics of Malaga goalkeeper Willy were a huge reason that the first leg ended goalless and the Argentine was at it again in the closing stages, denying both Reus and Gotze from close range
The home fans' misery looked to have been compounded in the 82nd minute as a swift break from the visitors ended with second-half substitute Eliseu sweeping home from close range.
Yet there was still time for one of the most dramatic comebacks in Champions League history, which Reus began as he slotted home following a long ball in the 91st minute.
Two minutes later the turnaround was complete and the stadium went from despair to unbridled jubilation.
Following a cross from the left a scramble in the area was put to an end when Santana swept the ball into the net from one yard out.
Somehow Dortmund, who will be joined in the semi-finals by Real Madrid, managed to keep their unbeaten home record in the tournament intact as their victory ended Malaga's fairytale run.