Michael Bournival also scored for Montreal (8-5-0), which has won three of its last four games.
Cody Eakin replied 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. Neither side had a lot of energy.
The Canadiens struck first as Raphael Diaz lofted a wrist shot from the point to the far post that Bournival tipped off defenceman Stephane Robidas and past Kari Lehtonen at 12:02 of the first. The rookie Bournival has three goals and four assists in his last seven games.
Bourque put in a Diaz rebound 12:55 into the middle frame.
Dallas struck back when Eakin used P.K. Subban as a screen and fooled Price with a medium speed 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.