Mike Ribeiro, in his regular-season return to Montreal, and Tom Wandell also scored for the Stars (30-26-4).
Carey Price stopped 33 shots for the Canadiens (24-27-10), who have lost four of five after a four-game winning streak.
The Stars took control in the first period, outshooting the Canadiens 15-6. The shots were 9-0 in favor of Dallas before Montreal recorded its first at 8:14.
For a fifth straight game, the Canadiens allowed their opponent to strike first when Garbutt, just called up from the minors, snapped a shot from the circle over a crouched Price.
The Canadiens had plenty of opportunities to tie it in the second period when Dallas was whistled for four consecutive penalties. Montreal had scored seven goals in its previous 25 power-play chances, but the Canadiens failed to net a man-advantage tally for just the second time in seven games.
Ribeiro, traded to Dallas for defenseman Janne Niinimaa on Sept. 30, 2006, put the Stars ahead 2-0 at 4:32 of the third. Dallas defenseman Trevor Daley found the former Canadiens forward with a cross-crease pass to the left of Price.
Just 37 seconds later, a clearing attempt by Price was intercepted, and the puck eventually found its way to Wandell in the slot.
NOTES: Canadiens C Tomas Plekanec missed the game because of the flu. Rookie Louis Leblanc returned after missing one game because of illness. ... The Stars scratched forwards Jamie Benn (lower body) and Adam Burish, and D Sheldon Souray (lower body). ... Canadiens D Chris Campoli's penalty midway through the third period snapped a streak of 5½ periods without an infraction against Montreal. ... The Stars haven't lost when leading after two periods since October 31, 2009 (59-0-6).