Colombia striker Falcao struck twice after the break for his eighth and ninth goals of the season to add to Rony Lopes's first-half opener.
Champions Monaco now have 15 points from six games and trail leaders Paris St Germain, who host Olympique Lyonnais on Sunday, on goal difference.
Top scorer Falcao now leads PSG's Edinson Cavani by two goals.
The principality side were thrashed 4-0 at Nice last weekend and, for a while, it seemed they had not fully recovered as they put on a mediocre display in the first half.
But Portuguese forward Lopes latched on to Falcao's cross in the 44th to put the home side ahead.
Falcao doubled the tally six minutes into the second half, poking home the ball from Jorge's cross.
The Colombian put the result beyond doubt in the 67th, firing a low shot past Bingourou Kamara after forcing his way past Kader Mangane.
(Reporting by Julien Pretot; Editing by Clare Fallon)
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