In one of the most enthralling endings to a Champions League tie, Dortmund secured a place in the semi-finals after two injury-time strikes saw off Malaga.
Joaquin and a superb Robert Lewandowski effort set up a tense second half but it was the Spanish club who looked set for a semi-final spot after Eliseu struck in the 82nd minute.
But there was more to come from the match as Marco Reus netted in the 91st minute before Felipe Santana popped up with the decisive goal just moments before the final whistle.
"Up until now, our story has been like a Hollywood movie - hopefully it will have a Hollywood ending," Dortmund defender Neven Subotic told Uefa.
"This is the craziest moment in all of my footballing career. It has been a special match for everybody - for us and the fans."
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