Riviere, who earned a place in the starting line-up because injuries had sidelined summer signings Joao Moutinho and James Roriguez, added three goals to Radamel Falcao's opener from the penalty spot.
Monaco are one of the four teams to maintain a perfect start along with Olympique Lyon, Olympique Marseille and St Etienne.
Falcao put Monaco ahead in the 18th minute following a Siaka Tiene foul on winger Lucas Ocampos in the box.
But his fellow Colombian Victor Hugo Montano levelled for the visitors six minutes later with a powerful header.
At the sun-baked Stade Louis II, Monaco took a decisive advantage thanks to Riviere's goals both sides of the interval.
He gave his side the lead in the 44th with a fine lob and made it 3-1 just before the hour by netting from a Yannick Ferreira-Carrasco corner kick.
The 23-year-old, who has never scored more than eight goals in a league season, headed his third of the day with eight minutes to go.
Champions Paris St Germain host Ajaccio in the day's late kick-off.