Price, who is 1-3-1 with a 4.41 goals-against average and .854 save percentage in his past five games, backed up Antti Niemi the previous two games.
The Canadiens have allowed at least four goals in seven of their past eight games, and are 4-5-1 in the past 10 after starting the season 5-1-2.
The Flames, who begin a four-game homestand, have scored four goals in the past three games (1-2-0) following a four-game winning streak.