Price notched his second straight strong game in goal for the Habs, following up on a shutout in Thursday's Game 1. He turned aside all 15 shots he faced in the first period when the Bruins came out strong and blanked Boston on four power-play opportunities.
Michael Cammalleri stunned Boston with a goal only 43 seconds into the game and Mathieu Darche added a power-play goal less then 2 minutes later as Montreal went on to sweep the first two games of their Eastern Conference quarterfinal series on the road.
Yannick Weber also scored for the Canadiens.
The Bruins were playing without defenseman Zdeno Chara, who was hospitalized with dehydration Friday. His loss seemed to rattle Boston, which made several costly turnovers in the defensive end.
Patrice Bergeron scored and Tim Thomas made 23 saves for the Bruins, who have never won a seven-game series after losing the first two contests in 26 all-time tries.