Joao Moutinho looked to respond for Monaco when he let fly with a long-range effort that skimmed over the crossbar.
Riviere was next to have a go as Monaco looked to dominate the first half, but he was denied by Benoit Costil, who tipped the ball away from his bottom corner.
Monaco continued to press for an opener before the break with Layvin Kurzawa seeing his effort saved in the centre of goal, while Riviere saw another attempt blocked just before the half-time whistle.
The visitors gained the lead their dominance deserved in the second half as Riviere was found by Jeremy Toulalan, leaving the striker to finish with his right foot across goal into the bottom left corner.
Geoffrey Kondogbia thought that he had put the game beyond doubt with just under 15 minutes remaining, but he saw his shot from distance palmed away by Costil as it looked headed for the top corner, leaving the final score to end 1-0.