A bumper crowd at the Stade Chaban Delmas came both to usher in the new Ligue 1 season and to check out the wealth of talent recruited by ambitious Monaco in the few months since their promotion in May.
Falcao was the star attraction while Joao Moutinho and James Rodriguez - captured together from Porto for 70 million euros - were in action. Jeremy Toulalan and Ricardo Carvalho also stepped out in principality colours, but it was the understated Riviere who finally opened the scoring nine minutes from time.
In the dying stages Colombian hitman Falcao, who had been bought on the strength of his formidable scoring record at Atletico Madrid and Porto, would deliver his first goal for Claudio Ranieri's men to rubber-stamp the victory.
Alexandre Lacazette scored twice as Lyon enjoyed the biggest winning scoreline of the first day of the Ligue 1 season with a 4-0 thrashing of Nice.
Lacazette opened the scoring after just 12 minutes but Remi Garde's side raced away with the match in the second half.
Clement Grenier added a second eight minutes after the break and Lacazette got his brace after 67 minutes with Yoann Gourcuff adding a stunning free-kick in injury time.
Valenciennes opened their season with an emphatic 3-0 win over 10-man Toulouse at the Stade du Hainaut.
The Nord region club impressed and surprised on their way to an 11th-placed finish last term and the early signs point to another successful season following tonight's one-sided encounter.
There appeared to be a case of mistaken identity when Uros Spajic was dismissed for a foul in the 35th minute. Maor Melikson converted the penalty but Steeve Yago had been the man under suspicion from the VA players in the build-up.
Perhaps rattled by the events of the first half, Toulouse allowed their hosts to pull away to a comfortable victory as Jose Saez and Gregory Pujol helped themselves to a goal each after the break.
A goal by Filip Djordjevic and a Julian Palmieri own goal saw Nantes claim a 2-0 victory over Bastia in their first match back in Ligue 1 as both teams finished the opening match of the season with 10 men.
Nantes' Jordan Veretout was given a second yellow card for arguing with the referee before Bastia were reduced to 10 men when Araujo Ilan was sent off for violent conduct.
Mevlut Erding scored a late winner as Rennes got a 2-1 victory against Reims.
Vincent Pajot put the home side ahead in the eighth minute but saw his early score cancelled out just before half-time by Grzegorz Krychowiak.
However, Erding ensured Rennes got their season off to a winning start when he slotted a low shot past Reims goalkeeper Kossi Agassa in the 84th minute.
Elsewhere, Divock Origi's first-half goal ensured that Rene Girard's reign as Lille manager got off to a winning start with a 1-0 victory against Lorient tonight.
Evian were unable to hold on to an early lead at the Parc des Sports as they drew their first match of the season 1-1 against Sochaux.
Fabrice Ehret put the home side ahead in the fourth minute and Evian kept the visitors at bay for 50 minutes before Roy Contout netted the equaliser.