Price turned aside a combined 18-of-18 shots in the first and third periods, allowing just a Cody Eakin goal in the middle period after the Canadiens had posted a 2-0 advantage.
The Habs goalkeeper improved his save percentage to an NHL-best .963.
Michael Bournival and Rene Bourque each scored for Montreal, which was coming off Monday's 2-0 shutout of the New York Rangers.
Kari Lehtonen made 22 stops for the Stars, who fell after defeating Buffalo 4-3 Monday.
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