The Colombia playmaker drilled home left-footed to put the hosts ahead after 18 minutes and then turned provider when his corner was headed in by Andrea Raggi to double the lead with 18 minutes remaining.
Rodriguez, who joined Monaco from Porto for a transfer fee of 45 million euros in the close season, fired in a penalty after 76 minutes for his ninth goal of the season, before Nantes grabbed a consolation through Alejandro Bedoya.
The win moved Monaco to 66 points, six clear of Lille in third but a long way adrift of leaders PSG, who beat Stade Reims 3-0 on Saturday thanks to an Edinson Cavani strike and two Aissa Mandi own goals.
St Etienne's Max Gradel scored an injury-time penalty to snatch a 1-1 draw with Nice on Sunday that left them five points adrift of Lille in fourth.
Fifth-place Olympique Lyon beat Valenciennes 2-1, in a game that included two red cards and a missed penalty.
Lyon's Remy Vercoutre and Valenciennes Marco Da Silva were then dismissed late on and the hosts' Abdul Majeed Waris failed to convert a penalty three minutes from full time.
- Sports & Recreation
- Andrea Raggi