Monaco cling on with 10 men to avoid French Cup shock
Elsewhere, goalkeeper Kjetil Haug stopped two spot kicks as Toulouse eliminated Angers in a shoot-out after the clash of Ligue 1 clubs ended 1-1.
In Orleans, Monaco, deprived of 10 key players, looked anxious and struggled to impose themselves.
Orleans squandered a couple of chances before Folarin Balogun converted one of Monaco's rare opportunities after 27 minutes.
After Monaco's Stanis Idumbo picked up a second yellow card in the 44th minute, the visitors sat back.
They survived several scares before 19-year-old George Ilenikhena, who had come off the bench to replace Balogun, struck in the 88th minute and again four minutes into added time.
Two minutes later Fahd El Khoumisti gave the hosts a consolation goal.
"The main thing was to qualify. The spirit of the team, playing 10 against 11, was remarkable," said Monaco coach Sebastien Pocognoli.
In Angers, Toulouse took the lead with a 47th-minute goal by Santiago Hidalgo following a Mark McKenzie long throw. The hosts levelled in added time with an Amine Sbai penalty.
In the shootout, McKenzie missed the first Toulouse penalty but after that his team were flawless while Haug saved the second and seventh Angers attempts.
The Saturday evening game between Ligue 1 leaders Lens and third-tier Sochaux was postponed because of snow.