Steven Stamkos had two goals and added an assist, and the Lightning beat the Canadiens 4-2 in a matchup of the Atlantic Division's top teams.
Both have 93 points, but Montreal has played one fewer game.
"It's definitely a confidence booster when you get the offense going in a game like this, especially down the stretch," Stamkos said.
Montreal, which lost for the sixth time in eight games (2-4-2), got goals from Tomas Plekanec and Pierre-Alexandre Parenteau.
"We started off slow," Montreal center Alex Galchenyuk said. "We didn't play a full 60 minutes, and that cost us."
Stamkos secured the win with his 39th goal, an empty-net, power-play goal with 1:05 to play. Filppula opened the scoring during a power play at 10:07 of the first, when his right circle shot was redirected by sliding Montreal defenseman Andrei Markov past Carey Price. Max Pacioretty made an ill-advised pass from neutral ice back into the Canadiens zone, and Stamkos stole it and made it 2-0 from the right circle with 4:02 left in the first.
"Funny things happen when we play Montreal," Tampa Bay coach Jon Cooper said. "It was a weird play."
Hedman put the Lightning up 3-0 after skating alone down the slot 2:45 into the second.
"They got a lucky bounce on the first goal. I gave them the second goal," Pacioretty said. "The third one was a good play. We played a good team game. Those things happen."
Plekanec tied Larry Robinson for 23rd place on the Montreal goals list, with 197, after a power-play tally at 11:10 of the second. Parenteau cut the Montreal deficit to 3-2 just 34 seconds into the third after Plekanec stole goalie Ben Bishop's pass behind the net.
"I didn't do us any favors turning the puck over," Bishop said. "After that, we kind of buckled down -- one of those things where you bend and don't break."
The Canadiens had P.K Subban's drive hit the post and Pacioretty's breakaway shot stopped by Bishop during a six-minute stretch after Parenteau's goal. Bishop, 9-1-2 against Montreal, made 32 saves. Price stopped 30 shots and is 10-10-5 against Tampa Bay.
Canadiens left wing Brandon Prust took part in two of the three fights and also got a goalie interference penalty after checking Bishop into the end boards.
"It's hockey," Cooper said. "Prust, that's what he does. He tries to get under a team's skin."
Chicago senior adviser Scotty Bowman, who coached the Canadiens to five Stanley Cups in the 1970s, was at the game. Montreal has won two NHL titles since Bowman left. ... Montreal D Alexei Emelin (shoulder) returned after missing 12 games ... Tampa Bay LW Ondrej Palat (lower body), D Braydon Coburn (lower body) and C Cedric Paquette (upper body) were out of the lineup. ... Canadiens C Torrey Mitchell (upper body) and D Nathan Beaulieu (flu) didn't play.