Leonardo Jardim's men were forced into a first-half change as Fabio Coentrao limped out of the game, but substitute Bernardo Silva almost made up for the Portuguese winger's departure when he delivered a menacing cross into Almamy Toure, but his header came back off the woodwork.
Traore almost broke the deadlock moments after the restart, but failed to convert his close-range effort.
However, the Ivorian finally gave Monaco the lead as he latched onto Fabinho's pass to score.
With six minutes left, he extended Les Rouges et Blanc's advantage when he reacted to Nabil Dirar's cushioned header and finished from a few yards out.
Julien Romain pulled a goal back for the Corsicans, but it proved to be too little, too late as Monaco go into fifth place.