Price stopped 29 shots for the Canadiens, who have lost four straight.
Brian Gionta scored with less than 2 minutes to go to spoil Fleury's bid for his 20th career shutout.
Pittsburgh rolled despite playing without star centers Sidney Crosby and Evgeni Malkin. Crosby continues his slow comeback from a pair of concussions that have sidelined him since January while Malkin is dealing with soreness in his surgically repaired left knee.
There remains no timetable for Crosby's return while Malkin is day-to-day.
Penguins veteran defenseman Brooks Orpik, who missed the first eight games of the season while recovering from abdominal surgery, returned last night and played nearly 18 minutes.
In other games *
At Boston, Zdeno Chara, Milan Lucic and Tyler Seguin had a goal and two assists each and the Bruins handed Toronto its first regulation loss, 6-2.
* At Tampa, Fla., Vincent Lecavalier had a goal and an assist to help the Lightning stop a five-game losing streak with a 4-1 victory over the New York Islanders.
* At Sunrise, Fla., Thomas Vanek scored two goals and Ryan Miller made 22 saves for his first shutout of the season in Buffalo's 3-0 victory over Florida.
* At Ottawa, Milan Michalek and Jason Spezza each had a goal and an assist in the second period to lift the Senators over Winnipeg, 4-1. Daniel Alfredsson scored in the third and Michalek scored his second of the game into an empty net.
* At Denver, Patrick Sharp broke a tie early in the third period and the Chicago Blackhawks went on to beat Colorado, 3-1, snapping the Avalanche's winning streak at five.
Jonathan Toews and Marian Hossa also scored and Corey Crawford made 30 saves to lead the Blackhawks.
* At Calgary, Ryan McDonagh scored with 2 seconds left in overtime to lead the New York Rangers to a 3-2 win over the Flames.
The Rangers got a shorthanded goal from Brandon Prust and a power-play goal from Marian Gaborik in a first period that ended tied at 2-all.
* At Glendale, Ariz., Dustin Brown and Kyle Clifford scored second-period goals and Jonathan Quick had 28 saves as the Los Angeles Kings shut out the Phoenix Coyotes, 2-0.
* At Edmonton, Dany Heatley tied the game with a third-period goal and Matt Cullen scored in the shootout as the Minnesota Wild defeated the Oilers, 2-1.
