Max Pacioretty and Torrey Mitchell also scored for the Canadiens, who stretched their team-record winning streak to start the season to seven game.
It broke the Blues’ (5-2-0) four-game winning streak.
Price, the league’s most valuable player and top goaltender last season, has allowed only six goals in six starts. It was the 36th shutout of his career.
He posted a 25-save shutout against the New York Rangers on Oct. 15.
His save of the night was a spectacular glove effort early in the second frame on Vladimir Tarasenko.