Marco Reus' double in the first half set up a potential shock comeback for Jurgen Klopp's men but they could not grab a third in the 2-0 win and ultimately crashed out, losing 3-2 on aggregate. Meanwhile, substitute Demba Ba knocked out Laurent Blanc's men at Stamford Bridge as Chelsea won 3-3 on aggregate thanks to the away goals rule.
Goal selects the best images from the evening's fixtures ...
Frank Lampard tussles with PSG midfield counterpart Blaise Matuidi in the middle of the pitch
Real Madrid started better, but a saved penalty gave BVB sudden impetus
Sure enough, Marco Reus scored the opener to set in motions a thrilling contest at Signal Iduna Park
Chelsea also scored in the first half as it aimed for its comeback, Andre Schurrle the scorer
Reus scored the second, too, for Dortmund as BVB fans' fantasy threatened to become reality
Schurrle raises his finger in celebration after giving Chelsea the lead
Oh Micky what a pity you don't understand, you break BVB hearts when you kick it in the stands
PSG goalkeeper Salvatore Sirigu stretches to try to keep Chelsea from progressing to the last four
PSG performed poorly on the night and Ba came off the bench to punish them with a late goal
Edinson Cavani suffered a similar fate at Stamford Bridge in the last eight with Napoli two years ago
It wasn't to be for Dortmund, as it valiantly exited to an undeserving Madrid side