Price logged his fourth shutout of the season and 23rd of his career in an effort that could cement his role as Team Canada's starting goalie in the upcoming Sochi Winter Olympics.
Rene Bourque scored in the second period and David Desharnais added an empty-netter as the Canadiens snapped the Flames' five-game winning streak.
Reto Berra, subbing for the Karri Ramo (knee), made 25 saves for Calgary.
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