The Blues were beaten by two second-half goals at Parc des Princes, while 2013 runners-up Dortmund face a mountain to climb to reach the last four at Real Madrid's expense.
Los Blancos never looked liked losing to last year's runner up, thanks to two first-half goals, while the Blues were let down by two second-half strikes which left them with a mountain to climb.
Goal selects the best images from the evening's fixtures ...
Ezequiel Lavezzi took just four minutes to put PSG into the lead with a stunning goal
Gareth Bale scored in the opening minutes for Real Madrid at the Bernabeu
Dani Carvajal looks like he's been dragged into karaoke by Xabi Alonso and Bale as they celebrate
Petr Cech punches the ball away from a fearless Thiago Silva, who went on to concede a penalty
The man who converted that penalty? Eden Hazard, who calmly buried into the bottom corner
Isco, given a starting spot in Angel Di Maria's absence, scored the second for Madrid
Heads up - Bale and Erik Durm do battle
After (probably) tapping Edinson Cavani on the shoulder, Gary Cahill ducks out of the striker's eyeline
Zlatan Ibrahimovic celebrates with Marco Verratti and Thiago Motta following David Luiz's own goal
Cristiano Ronaldo takes a quick breather as he looks to equal Lionel Messi's Champions League record
On 57 minutes the forward drew level with Messi for goals scored in a single Champions League campaign
Zlatan Ibrahimovic pulled up with a nasty-looking hamstring injury in the second half
Is there a photo of Marcelo leaping over his teammates in every game Madrid win?
When Javier Pastore scored PSG's third in stoppage time, Jose Mourinho walked off in defeat
Klopp will be hoping he can wipe that smile from Carlo Ancelotti's face next Tuesday