The visitors established control of possession early and opened the scoring just seven minutes into proceedings.
Having seen his shot deflected behind for a corner, Nuno Mendes played the ball short before delivering an exquisite cross that Willian Pacho headed in for his first-ever PSG goal.
Die Werkself still caused problems with Claudio Echeverri playing a central role, and his tenacity forced Ilya Zabarnyi into a handball to concede a penalty, but Alejandro Grimaldo smashed his spot-kick against the post.
The hosts’ cause seemed to be seriously damaged when Robert Andrich was sent off for elbowing Desire Doue in the face, but Zabarnyi pulled down Christian Kofane just five minutes later to receive a red card and concede a second penalty, which Aleix Garcia slotted into the bottom corner.
Undeterred, PSG reestablished their lead just three minutes later when Doue finished a lovely move by playing the ball out to Khvicha Kvaratskhelia and getting it back before guiding his shot out of Mark Flekken’s reach.
Another three minutes brought another PSG goal, with Kvaratskhelia having one shot blocked and sending another in off both posts.
PSG still found time to score once more before the break, as a swift move culminated in Doue working space on the edge of the box and picking out the bottom corner.
They had another within five minutes of the restart, with Vitinha slipping through Nuno Mendes for the left-back to beat Flekken despite the goalkeeper getting a hand to his shot.
Garcia then sent an outrageous strike into the top corner in a rare moment of respite for the hosts, but that would be fleeting as Barcola selflessly set the returning Ballon d’Or winner Ousmane Dembele to score just three minutes into his return from injury.
Vitinha then rounded off the evening with a superb strike from range, as PSG emphatically recorded a fifth consecutive Champions League victory to equal their longest winning run in European football’s top competition.
They also inflicted Kasper Hjulmand’s first loss at Bayer Leverkusen, leaving Die Werkself with just two Champions League points.
Flashscore Man of the Match: Vitinha (Paris Saint-Germain)