Brad Richards and Filip Kuba also scored for the Lightning, who outshot Montreal 41-13. Tampa Bay was coming off a 4-3 loss Thursday to Philadelphia, which had lost 10 straight and has the NHL's worst record.
The Canadiens' record for fewest shots in a game is 12, coming twice against Ottawa on Jan. 26, 2006 and Dec. 27, 2002.
Montreal goalie Cristobal Huet made 38 saves. Alexander Perezhogin scored for Montreal.
Tampa Bay goalie Johan Holmqvist turned aside 12 shots.