Nikita Kucherov scored twice on power plays,
Jeff Petry and
Tampa Bay went four for seven on the power play, and Montreal was 0 for 3.
Filppula and Hedman scored with the man advantage as Tampa Bay got its first power-play goals since Game 2 of its seven-game opening series against Detroit.
Montreal is one for 26 with the man advantage in the playoffs.
The Canadiens scored the first goal of a game for only the second time in eight postseason contests, when Petry took a pass from
Montreal let it slip away with undisciplined penalties.
Stamkos used a fortunate bounce to go in on a breakaway and deke Price for a goal 8:06 into the second. It was the Lightning captain's first goal in nine postseason games this year. He also had two assists.
The Lightning had a four-on-three man advantage when
Kucherov redirected Johnson's pass inside the post 6:37 into the third to make it 5-1, before Gilbert scored from the point at 11:06 for Montreal. Brown added his goal at 16:05.
Prust got a game misconduct with 3:55 left. He bumped Bishop, leading to a fight with Braydon Coburn.
at Chicago 4, Minnesota 1: Patrick Kane scored two goals, Corey Crawford made 30 saves and the Blackhawks took a 2-0 lead in the Western Conference semifinals.
Patrick Sharp had a goal and an assist as Chicago improved to 5-0 at home in this year's playoffs. Jonathan Toews also scored in the second after a big play by Marian Hossa.