Marseille had begun their season with three straight wins in the league and looked on course for a fourth when Brazilian defender Lucas Mendes gave Elie Baup's men a 43rd-minute lead.
However, Monaco drew level through one of their big-money summer signings, Radamel Falcao, two minutes after the interval, while Riviere settled the contest six minutes after being introduced off the bench.
St Etienne continued their good start to the domestic campaign and made slight amends for the Europa League exit in midweek by edging out Bordeaux 2-1.
Les Verts were eliminated from the Europa League after being edged out 5-3 on aggregate by Danish side Esbjerg in their play-off encounter, but they took a seventh-minute lead through Romain Hamouma.
Loic Perrin doubled the lead five minutes into the second half, with Ludovic Obraniak's stoppage-time goal scant consolation for Les Girondins.
Nice twice let a goal-lead slip in their 2-2 draw at home to Montpellier.
The hosts led twice during the game, with Timothee Kolodziejczak and Valentin Eysseric having efforts cancelled out by Souleymane Camara and Siaka Tiene before Montpellier's Djamel Bakar was sent off late on.