PSG, who clinched a fourth consecutive league title last weekend, succombed to second-half goals by Vagner Love and Fabinho as they slumped to their first league defeat at the Parc des Princes since losing 2-1 to Stade Rennes on May 7, 2014.
The capital club, hoping to break their record of 89 points in a season, have 77 points with seven matches left, while Monaco are on 55 points and lead Nice, who beat GFC Ajaccio 3-0, by five points and fourth-placed Olympique Lyonnais by six.
Lyon won 2-0 against visiting Nantes on Saturday.
PSG's defeat means Nantes remain the only side to have lost one game in a single French top-flight season back in 1994/95.
They remain on course for a quadruple, however, after reaching the French Cup semi-finals, League Cup final and Champions League quarter-finals.
Laurent Blanc's side dominated the first half but Monaco's steely defence held firm and the visitors looked much sharper after the break.
In the 65th minute, Love latched on to a fine cross from the left by Thomas Lemar to open the scoring. Three minutes later, Fabinho wrapped up the points with a penalty after David Luiz brought down his fellow Brazilian in the box.
Ligue 1 top scorer Zlatan Ibrahimovic came close to reducing the arrears but his header shaved the crossbar and the Swede then fired a sitter over the bar.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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