Monaco are still yet to taste defeat since earning promotion from Ligue 2 last season, but paid a heavy price for their win as star striker Radamel Falcao suffered an ankle injury in the second half.
Marseille went in front just a minute before the interval as Lucas Mendes headed in Mathieu Valbuena's corner.
However, their advantage did not last long, Falcao equalising early in the second period with his third goal of the season.
The Colombian did not finish the match, but his replacement Emmanuel Riviere scored the winner with his fifth of the campaign.
Riviere - signed from Toulouse in January - slotted home after latching on to a superb through-ball from Joao Moutinho.
Saint-Etienne bounced back from their defeat at Lille last week as they beat Bordeaux 2-1 at the Stade Geoffroy Guichard.
Romain Hamouma gave the hosts the lead after seven minutes when he converted Banel Nicolita's right-wing cross, before Loic Perrin's header effectively wrapped things up five minutes into the second half.
Ludovic Obraniak's late goal proved to be nothing more than a consolation for Bordeaux, who have won just one of their opening four games.
Nice played out an entertaining 2-2 draw in their final game at the Stade du Ray before moving into the newly-built Allianz Riviera.
Left-back Timothee Kolodziejczak put Claude Puel's men in front with a glancing header, before the 2011-12 champions levelled through Souleymane Camara.
Valentin Eysseric restored Nice's advantage two minutes before the break, but they could not hold on to claim the points as Siaka Tiene equalised again for Montpellier, who clinched a share of the spoils despite Djamel Bakar's late dismissal.
