The former Manchester United forward settled a tight encounter when he netted his 14th goal of the season -- his 11th in Ligue 1 -- with eight minutes remaining at the Stade Velodrome.
It came just moments after Folarin Balogun thought he had given Monaco the lead, but his effort was ruled out by VAR for offside.
Greenwood buried a first time shot from just inside the area after being slipped in by Pierre-Emile Hojbjerg.
He was booked for taking his shirt off in the celebrations that followed, but Marseille held on for a result that kept them within five points of leaders Lens.
Marseille may feel victory was deserved on the balance of play, but Monaco matched them when it came to opportunities.
Pierre-Emerick Aubameyang and Timothy Weah forced early saves from Monaco goalkeeper Lukas Hradecky, but Aleksandr Golovin and Takumi Minamino had chances at the other end.
Greenwood twice missed the target and Minamino had further efforts for Monaco before Igor Paixão drew a save from Hradecky.
Hradecky then saved twice from Greenwood and it seemed Marseille would pay the price as Balogun found the net 10 minutes from time but the goal was chalked off.
Greenwood, who scored two against Union Saint-Gilloise in the Champions League on Tuesday, made no mistake with his next opportunity as he fired Marseille into a late lead.
George Ilenikhena had a chance to level in the last minute for Monaco but could not beat Gerónimo Rulli.
