Riviere, who earned a place in the starting line-up because injuries had sidelined summer signings Joao Moutinho and James Rodriguez, added three goals to Radamel Falcao’s opener from the penalty spot.
Monaco were 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 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.
In the Netherlands, striker Kolbeinn Sigthorsson scored both goals as champions Ajax won an early-season meeting with arch rivals Feyenoord 2-1. Ajax recovered from a goal behind to win the match regarded as the Dutch league season’s “classic” to claim a second win in three matches this new season. The defeat plunged Feyenoord into crisis after a third successive loss – their worst ever start to a season.
PSV Eindhoven and PEC Zwolle are the early-season leaders in the Dutch league with 100 per cent starts after wins on Saturday.
In Germany, Hiroshi Kiyotake curled in an 89th-minute free kick to give Nuremberg a 2-2 draw at home to promoted Hertha Berlin in the Bundesliga after the visitors had gone ahead with a controversial penalty.
Nuremberg made the breakthrough five minutes before half-time when Daniel Ginczek won possession and threaded the ball through for Josip Drmic to stroke past Hertha goalkeeper Thomas Kraft.
Hertha, who started their campaign with a 6-1 demolition of Eintracht Frankfurt last week, looked set to make it six points from their opening two games when they turned the game around after half-time.
They levelled just after the hour when a Sami Allagui shot took a wicked deflection off the helpess Berkay Dabanli before substitute Ronny converted a penalty, awarded for a foul by Javier Pinola on Alexander Baujohann, with 11 minutes left. Nuremberg protests that Pinola had played the ball were forgotten when Kiyotake’s brilliant effort gave Nuremberg their second consecutive draw of the campaign.