Monaco twice came from behind and needed an 86th-minute winner to claim a 3-2 win at third-division Vannes in the ninth round of the Coupe de France.
Hendrick Cakin put the underdogs in front after only two minutes, only for Radamel Falcao to level a minute later.
Yannick Aguemon restored the hosts' lead in the 36th minute, but Monaco equalised again through James Rodriguez three minutes before half-time.
And the visitors grabbed the winner late on thanks to substitute Yannick Carrasco.
Lille also had to survive a scare on the way to winning 3-1 at third-tier Amiens.
Nordine Benaries had the hosts dreaming of a shock with the opener after six minutes, but Salomon Kalou struck either side of half-time to turn the match around.
Ronny Rodelin added a third in the 65th minute to seal the visitors' progress.
Lyon enjoyed far easier passage as they hammered lowly La Suze 6-1.
The Ligue 1 side only led 2-1 at the break thanks to goals from Bafetimbi Gomis and Clement Grenier either side of Nicolas Pichot's penalty.
But Lyon ran away with it in the second half as Gomis got his second, Alexandre Lacazette scored twice and Steed Malbranque also netted.
Marseille needed extra time to beat Reims, a double from Andre Pierre Gignac earning them a 2-0 win.
Nice were 2-0 winners at Nantes, with Didier Digard and Christian Bruls on target.
Bastia won 1-0 at home to Evian thanks to Florian Raspentino's goal.
Elsewhere, Bordeaux won 2-1 at Raon-l'Etape, Ajaccio won 2-1 at Quimperle and Montpellier earned a 2-0 success at Rodez Aveyron.
Guingamp, L'lle-Rousse, IC Croix and Sete also went through.