PSG needed penalties to beat Montpellier on Thursday (AEST), though Monaco got the job done in the allotted 90 minutes, with Cesc Fabregas delivering a star turn.
Indeed, Monaco had to come from behind after Alexis Peuget's fine opener, but Arthur Bozon's calamitous own goal and Aurelien Tchouameni's header put Niko Kovac's team in control.
Wissam Ben Yedder's 21st goal of the season dashed any lingering comeback hopes, and Rumilly Vallieres' incredible run came to an end with a whimper as Fabregas – who provided two assists – curled in an exquisite free-kick before Aleksandr Golovin finished things off.
Eager to make the most of an unprecedented opportunity, Rumilly Vallieres had their reward for a bright start in the 20th minute.
Djibril Sidibe's awful clearance put Monaco in trouble, with Joris Cottin laying it off for Peuget, who dispatched a brilliant 20-yard strike into the top-left corner to leave the visitors stunned.
Yet it was a lead which lasted just seven minutes, and was cut in a humiliating fashion – Bozon directing what would have been a perfect diving header at the other end into his own net.
Rumilly Vallieres were behind within five minutes, Dan Delaunay failing to keep out Tchouameni's header despite getting a hand to the ball, and matters would have been made worse for the minnows had Kevin Volland performed the simple task of finishing into an empty net from six yards out, only for the German to hit the crossbar.
Having set up Volland's chance, Ben Yedder made no such mistake, combining with Fabregas before lifting a delicate finish over Delaunay.
Jocelyn Gay went close with a rasping strike, but Rumilly Vallieres were out of ideas, and Monaco's fourth came from the brilliant Fabregas, who sent a wonderful free-kick into the top-left corner.
Further damage came four minutes later, substitute Golovin racing through and slotting home to seal Monaco's progression in emphatic fasion.