Louis Leblanc and Lars Eller both scored in regulation for the Canadiens, who have won their past two. Price made 32 stops in the win.
"I thought we played well the whole game," said Plekanec. "We tried to shut them down. We we're able to get two points. That's the most important thing."
"We were able to get the game even on Neal's goal," said Pittsburgh head coach Dan Bylsma. "Then we had to kill a penalty to get a point and it was a big point. Would have been better to get both points because you don't feel good when you lose a shootout."
The first 20 minutes passed scoreless as Price stopped 11 shots and Fleury made 10 saves.
Montreal, though, got on the board at the 11:21 mark of the second when Leblanc got the puck inside the Pittsburgh zone and from the inside right circle beat Fleury cleanly with a shot.
Pittsburgh tied the game 63 seconds into the third while shorthanded as Joe Vitale's pass from the right wing to the front of the net went off the right skate of Dupuis and past Price.
Montreal took the lead back as Eller's easy shot from the left point fooled Fleury at the three-minute mark.
However, the Pens tied the game 4 1/2 minutes later as Evgeni Malkin sent a pass from behind the net that deflected off the stick of a Hab and went right to Neal, who used the one-timer from the low left side for his 28th of the year.
Montreal plays in New York against the Islanders on Thursday...Pittsburgh has off until Saturday when it will host Winnipeg...This was the last game between these two this season. Montreal avoided the sweep as the Penguins had won the previous three.