Plekanec skated straight in on Fleury and buried a forehand shot high to the glove side that found the upper corner of the net.
Montreal's Carey Price made the advantage hold up when he made a sprawling pad save on a low forehand shot from Jason Williams, and the Habs bested the Penguins for the first time in four meetings this season.
Lars Eller and Louis Leblanc scored in regulation. Price made 32 stops for Montreal.
Fleury finished with 28 saves.