After Cole Caufield's shot went off the left post at 7:24, the Canadiens gained some momentum, and Danault cut the lead to 2-1 at 11:16 when he scored his first of the playoffs on a wrist shot from the left side as Brendan Gallagher drove to the net.
"We got a power play and scored right away, so a tremendous start," Hedman said. "Then I think they kind of took over in the first. We came out with the lead, so it was a good start and I thought we set the tone. But I thought it got better in the second and it was more consistent on our part."
Kucherov made it 3-1 with his eighth goal of the postseason at 1:40 of the second period. Lightning defenseman Erik Cernak hit Ondrej Palat at the Canadiens blue line with a stretch pass to set up a 2-on-0, and Kucherov scored with a backhand.
Kucherov got his 24th assist on Hedman's goal and leads the playoffs with 32 points.
"We have a game plan and everybody's buying in and everybody's doing their job," Kucherov said. "And when everybody's doing their job, it makes it easier. And we want to play a full 60 minutes the right way, and that's what we're doing right now."
Johnson put Tampa Bay up 4-1 at 3:33, but Suzuki drew Montreal within 4-2 at 18:04 with a wrist shot under Vasilevskiy's right pad from the right side.
Johnson scored his second of the game at 15:19 of the third period to make it 5-2. Perry cut it to 5-3 at 15:58 with Price pulled for an extra skater, but Blake Coleman scored into an empty net at 16:48 for the 6-3 final.
"We put ourselves in a hole early, and it's tough to dig yourself out of a hole against a team like that, that plays pretty stingy," Canadiens captain Shea Weber said.
NOTES: Vasilevskiy has won 11 straight games against the Canadiens, regular season and playoffs combined, since Feb. 24, 2018, the third-longest streak by a goalie against Montreal. Turk Broda of the Maple Leafs (Dec. 9, 1939-Jan. 23, 1941) and Alec Connell of the Ottawa Senators (Feb. 28, 1925-Feb. 22, 1927) each had 12 consecutive wins against the Canadiens. … The Kings are the only other team to take a 3-0 series lead in the Cup Final in the past 22 years. Los Angeles did so twice, in a six-game win against the New Jersey Devils in 2012 and in a five-game win against the New York Rangers in 2014.