Price, who is 299-209-66, all with Montreal, is 5-0-0 with a 2.30 goals-against-average in his past six games (five starts).
Montreal has won two straight and is 5-1-0 in its past six games. The Canadiens have scored at least four goals in four of their past six games.
Jaroslav Halak will start the second of back-to-back games for Boston, which is trying to avoid a third consecutive loss after winning three in a row.
Tuukka Rask made 23 saves in a 4-2 loss to the Buffalo Sabres on Sunday.
The Bruins, who are 3-5-0 in their past eight games, have scored two goals or fewer in 11 of the past 15.