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 and ultimately crashed out, losing 3-2 on aggregate. Meanwhile, substitute Demba Ba knocked out Laurent Blanc's men at Stamford Bridge as Chelsea went through on away goals after drawing 3-3 on aggregate.
Goal selected the best images from another crazy night of European football...
Frank Lampard tussles with PSG midfield counterpart Blaise Matuidi
Real Madrid started better, but a saved penalty gave BVB some added 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 they aimed for their comeback, Andre Schurrle the scorer
Reus also scored Dortmund's second as the German side closed in on an unlikely comeback
Schurrle raises his finger in celebration after giving Chelsea the lead
Mkhitaryan worried Madrid's defenders all night but wasted several chances
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 they valiantly exited to a below-par Madrid side