The German club won the second leg of their quarter-final tie 3-2 at home to reach the last four of the competition by the same aggregate scoreline, thanks to Felipe Santana's injury-time goal.
© PA Photos
Jurgen Klopp's side did not panic and restored parity six minutes before the interval through Robert Lewandowski. Lukasz Piszczek and Mario Gotze linked up with each other to release Marco Reus, who flicked the ball with his heel to the Polish striker to tap home from close range.
Last season's German champions came out in force in the second half, Lewandowski forcing Wilfredo Caballero into a save immediately after the restart.
Two minutes later Roman Weidenfeller kept out a close-range header from Joaquin with a good save, before Gotze shot wide for Dortmund from a narrow angle.
Lewandowski thought that he had scored his and Dortmund's second goal of the evening midway through the second half, but his effort was ruled out as Reus was in an offside position during the buildup.
© AP Photos
Dortmund pressed on and got their equaliser in the first minute of injury time through Reus, who slotted home after some good work from Neven Subotic.
Then two minutes later Santana tapped in from close range to seal a dramatic 3-2 win for the German club and a place in the semi-finals.