Montreal was shut out for the first time this season in its 69th game.
"We worked hard, we had chances, we had everything, but we didn't have a finish," Canadiens coach Claude Julien said. "We couldn't score. I think the 4-0 kind of score doesn't tell the tale of the game except that they were a way more talented team than we [were] as far as a lineup was concerned."
Hedman gave the Lightning a 1-0 lead at 49 seconds of the first period from the high slot, his first goal since Dec. 23. He went 31 games without one.
"[Hedman is] a world-class defenseman, I think he's the best in the League," Lightning defenseman Mikhail Sergachev said. "He does everything well. 5-on-5, 4-on-5, 5-on-4, he's just a rock. It's great to have a player like that on the team."
Alex Killorn made it 2-0 at 12:40 when he finished a 2-on-1.
"We were a little sloppy early, especially in the first period," Canadiens defenseman Shea Weber said. "But we gave them … a high-powered offense … you can't give them 2-on-1s and easy goals like that."