Rodriguez, who netted his first of the season when he opened the scoring in Saturday's 2-0 home win over Rennes, put Monaco ahead after five minutes in Nice.
Striker Emmanuel Riviere headed their second in the 23rd from Anthony Martial's cross and Lucas Ocampos added the third just before fulltime.
Monaco stay third but now have 35 points from 16 games behind PSG, who visit Evian TG on Wednesday.
"I'm really satisfied because we played well, we controlled the play," coach Claudio Ranieri told broadcaster Canal Plus.
"With the new system, our defence has more support. But it's the mentality that counts, not the tactics," added Ranieri, whose team have won all three matches played since he gave up using two wingers and started Rodriguez as a playmaker.
Monaco are one point behind second-placed Lille, who beat Marseille 1-0 thanks to an added-time goal by Nolan Roux. Marseille remain in fourth place on 27 points.
Lille's Nigeria goalkeeper Vincent Enyeama produced a sterling performance and has not conceded a goal in 1,035 minutes as they recorded an 11th consecutive clean sheet.
In Nice, Rodriguez converted his first chance with a curling shot after Joao Moutinho set him up down the right wing.
Led by Rodriguez and 17-year-old Martial, who was starting his second straight league game up front in Radamel Falcao's absence with injury, Monaco pushed for a second goal and were rewarded when Riviere finished off a fine collective move.
The principality club controlled the play and substitute Ocampos wrapped up the victory as Monaco inflicted a sixth consecutive league defeat on Nice.