Fleury did not allow a goal until Brian Gionta beat him with a slap shot with 1:36 to play in the third period.
The Penguins won their second in a row and handed the Canadiens their fourth consecutive loss. Montreal has just one win in six games this season.
James Neal put Pittsburgh in front midway through the first period with his seventh goal of the season. Joe Vitale and Arron Asham both tipped in a shot to produce their first goals -- Vitale's coming 2:39 into the second and Asham's 5:20 into the third.
Carey Price made 29 saves for Montreal, but saw his record drop to 1-4.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
Man behind Doritos Locos Tacos passed away on Thanksgiving