Miller made 26 of his saves during the final two periods, including 11 down the stretch for the Sabres, who rebounded from a 1-0 deficit and notched their fourth win in five games to start the season.
Rookie Swiss defenseman Raphael Diaz got the only marker for Montreal, which opened with four losses in five games for the first time since 1999-2000.
Carey Price stopped 20-of-22 shots for the Canadiens.
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