Michael Bournival also scored for Montreal (8-5-0), which has won three of its past four games.
Cody Eakin scored for Dallas (5-6-1), which remained last in the Central Division.
Dallas outshot the Canadiens 27-24.
Both teams had played the night before, with Montreal winning 2-0 in New York and the Stars taking a 4-3 decision in coach Lindy Ruff's return to Buffalo.
The Canadiens struck first as Raphael Diaz lofted a wrist shot from the point to the far post that Bournival tipped off defenseman Stephane Robidas and past Kari Lehtonen at 12:02 of the first.
Bournival has three goals and four assists in his past seven games.
Bourque put in a Diaz rebound 12:55 into the second period.
Dallas struck back when Eakin used P.K. Subban as a screen and fooled Price with a wrist shot from outside the circles at 17:27.
The Stars pressed for the equalizer in the third period, but ran into a Montreal side playing conservative, defensive hockey.
Notes: Travis Moen, who took a puck in the face Saturday, sat out a second game, so Louis Leblanc played. ... Montreal's injured include Max Pacioretty, Daniel Briere, Brandon Prust and Alexei Emelin. ... Ryan Garbutt, Kevin Connauton and Travis Morin were scratched for Dallas. ... Ryan White and Michael Blunden each played his 100th NHL game.
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