The Canadiens were coming off a 2-0 victory against the Rangers in New York on Monday night with Peter Budaj in goal.
"The last two games it's been really good team defense, whether it's getting pucks out or blocking shots or just being in position," defenseman Douglas Murray said. "It was a good effort by the whole team."
"With the fact that we're missing some players, we have to concentrate on good defensive play and we did that tonight," Therrien said. "I like the effort everyone is giving us.
"Carey [Price] made the saves. It was a big team win. That's four big points in two nights."
Dallas outshot Montreal 27-24, but managed only Cody Eakin's goal on a long shot that fooled Price late in the second period.
The Stars, last in the Central Division at 5-6-1, were also playing a second game in as many nights, having topped the Sabres 4-3 in coach Lindy Ruff's return to Buffalo on Monday.
It was their third set of back-to-back games this season. In one they lost both games and in the other two they won the first game, but lost the second.
"We've got to start finding a way in back-to-backs, especially on the road," Eakin said. "It's hard, yeah, but to be a good team you have to do it.
"These points are huge. They're harder to get as the season progresses, so we have to start bearing down."
Eakin used P.K. Subban as a screen on a rush and fooled Price with a wrist shot from outside the circles at 17:27 of the second to draw the Stars to within one goal.
"It was one of those ones where I used him as a screen," Eakin said. "I had some speed and caught him off guard a bit."
The Stars pushed hard for the equalizer in the third, when they outshot Montreal 9-3, but Price stood his ground.
The Canadiens struck first as Raphael Diaz lifted 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. The rookie Bournival has three goals and four assists in his past seven games.
"I wasn't sure if I deflected it," the 21-year-old said. "I felt it on my stick, but I didn't want to say anything."
Bourque put in a Diaz rebound 12:55 into the second.
David Desharnais started the play with a rush up the right side that was stopped. A Dallas clearing attempt was intercepted by Diaz, who picked up his second point of the night.
Desharnais has no goals and one assist in 13 games, but the line did well and Therrien gave them more ice time than usual.
"We were moving our feet," Bourque said. "We finally got a few chances offensively.
"Davy and I have been snake-bitten, but we're getting chances."
Travis Moen, who took a puck in the face Saturday, sat out a second game. ... Ryan Garbutt, Kevin Connauton and Travis Morin were scratched for Dallas. ... Montreal's Ryan White and Michael Blunden each played his 100th NHL game.