Monaco remain five points behind reigning champions PSG, who beat Valenciennes 3-0 on Friday.
Colombia attacking midfielder Rodriguez opened the scoring on the stroke of half time, with the former Porto man curling a free-kick into the top corner.
And the 22-year-old made sure of the points in the 77th minute as he finished off an excellent counter-attack to condemn Bastia to only their second home loss of the campaign.
UEFA Europa League outsiders Reims continued their superb season with a 1-0 win over Bordeaux.
Striker Nicolas de Preville scored the only goal of the game in the 64th minute as Reims leapfrogged Lyon and Marseille into fifth place.
Sochaux's survival hopes were handed a boost thanks to a 1-0 success against Guingamp, secured by a late strike from Zambia defender Stopilla Sunzu.
Sunzu powered home a diving header in the 84th minute to clinch Sochaux's fourth win of the campaign.
Toulouse moved into the top half after Alain Casanova's side came from behind to win 3-1 at Lorient.
The hosts were reduced to 10 men after 24 minutes when midfielder Alain Traore was sent off for a late challenge on Abel Aguilar, but Toulouse did not make the numerical advantage count and fell behind as Lorient defender Wesley Lautoa found the net four minutes before the break.
The visitors turned things around with an excellent second-half display though, with Wissam Ben Yedder levelling before goals from defender Serge Aurier and striker Martin Braithwaite ensured their triumph.
A 90th-minute strike from Souleymane Camara earned Montpellier a 2-2 draw at Rennes.
Ola Toivonen put Rennes ahead after 10 minutes, only for Daniel Congre to equalise nine minutes into the second half.
The Sweden striker looked to have sealed the victory for Rennes with a second goal in the 65th minute but Montpellier refused to be denied and claimed a point as Camara headed home Remy Cabella's cross at the death.
Nice and Nantes played out a 0-0 draw in Saturday's other match.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
Get FourFourTwo Newsletter
The best features, fun and footballing quizzes, straight to your inbox every week.