Monaco goalkeeper Danijel Subasic gave away a penalty midway through the first half but saved Serge Gakpe's spot kick.
Falcao, who missed out on helping Rodriguez lead Colombia to the World Cup quarter-finals because of injury, is still feeling his way back to full fitness but planted an unstoppable header into the net on the stroke of halftime.
Monaco are 17th in the table, which is led by Bordeaux after Saturday's 3-1 victory at Nice made it three wins out of three. Stuttering champions and title favourites Paris St Germain are sixth on five points following Friday's 0-0 draw at Evian.
In Ligue 1’s other games, Lyon lost at home to Lens, with Lalaïna Nomenjanahary on target, while the match between St Etienne and Rennes ended in a 0-0 draw.
- Sports & Recreation
- James Rodriguez
- Real Madrid
- Serge Gakpe