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 the Canadiens.
Tampa Bay goalie Johan Holmqvist turned aside 12 shots.
Prospal gave the Lightning a 2-1 lead on his backhander from near the goal-line between the net and the boards with 13 minutes left in the second. It was his first goal since Nov. 15, which also came against Montreal.
Kuba made it 3-1 on the power play at 7:07 of the third.
Huet kept the Canadiens in the game by stopping 22 of 23 shots in the first. The only goal he allowed came on Richards' rebound during a power play at 11:28.
The 23 shots allowed by Montreal during the first were a season-high. The Canadiens tied a season-low by taking just three shots in the opening period.
Montreal tied it at 1 when Perezhogin scored on the Canadiens' first shot of the second at 2:07. It was his first goal in 12 games.
Huet stopped 11 more shots in the second, including Vincent Lecavalier during a 3-on-1.
Notes: The most shots allowed by Montreal during one period since 1955 is 24, which has occurred four times. ... Philadelphia claimed LW Dmitry Afanasenkov off waivers from the Lightning. ... Lightning D Paul Ranger (hand) was out of the lineup.