Midfielder Lamine Camara curled the ball in from the edge of the penalty area after receiving a pass from Breel Embolo as unbeaten Monaco moved onto 16 points after six rounds.
Marseille are also unbeaten but need to win at Strasbourg on Sunday to join the top two.
At Stade Louis II, the home side fell behind to Rabby Nzingoula's early goal after losing the ball in midfield.
United States forward Folarin Balogun latched onto Embolo's reverse pass to equalise in the 32nd minute with his second goal in as many games.
Elsewhere, Jonathan David scored a hat-trick as 2021 champions Lille won at Le Havre 3-0.
David was widely expected to join a big European club after scoring 52 goals for Lille in the past two seasons. But the lure of playing regular Champions League soccer this season saw him stay in northern France.
His two first-half goals were set up by Norway left winger Osame Sahraoui - a summer signing from Dutch side Heerenveen - and his third goal was assisted by Kosovo right winger Edon Zhegrova.
David has seven goals this season.
There were no scoring feats in Saturday's other game as Nice drew at Lens 0-0.
Nice's attack was kept in check a week after an 8-0 rout of Saint-Etienne. In fact, Nice goalkeeper Marcin Bulka earned his team a point.
Lens forward Anass Zaroury was sent off late on.
In a touching moment for Nice coach Franck Haise, he was loudly applauded by Lens fans when his name was read out before the game.
Haise coached Lens from 2020-24 and guided the working-class club back to the Champions League during his tenure.
PSG beat Rennes 3-1 on Friday.
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