Carey Price recorded a leisurely shutout, stopping 19 shots fired by the punchless Senators. Price faced only four shots in the first period and three in the final frame.
The second period was a penalty-filled affair in which Jeff Halpern and Jarkko Rutu squared off and both received 5-minute fighting majors.
The win gave the Canadiens victories in both of their first two contests against the Senators this season, during which the teams will meet six times.
The Senators' Brian Elliott absorbed the loss, allowing all three goals on 34 shots.