"We had the puck a lot because we were smart with it in the neutral zone," Stamkos said. "It allowed dominating shifts in their defensive zone."
"They know how to put the puck in the net," Nilsson said. "That's a good team over there. I felt OK but obviously none of us were good enough."
Kucherov opened the scoring on his 28th goal by converting a rebound 14:36 into the first period.
"You're not going to keep a kid like that down for long," Stamkos said. "It was a matter of time. You could tell by his celebration he was happy to score."
After Gourde got his 20th goal during a power play at 1:38 of the second, Erne made it 3-0 with 6:20 left in the second in his first NHL game this season.
The Lightning recalled Erne from Syracuse of the AHL before the game.
"I was a little nervous in the beginning," Erne said.
Stamkos completed Tampa Bay's three-goal second when he picked his up 20th goal late in the period.
"I didn't think our first two period were as bad as the score, Canucks center Henrik Sedin said. "It should not have been 4-0 after two periods. Daniel (Sedin) has a couple of good chances and we just don't score."
Boeser, the MVP at last month's NHL All-Star game in Tampa, had a power-play goal early in the third.
Sven Baertschi cut the deficit to 4-2 midway through the period.
Hedman had a late power-play goal.
Canucks C Sam Gagner, with a sprained ankle, sat out. ... Vancouver C Brenden Gaunce will miss two to four weeks with a foot injury. ... Tampa Bay D Dan Girardi returned after missing three games due to a lower-body injury. ... The Lightning have out scored their opponents 73-45 in the second period. ... Gourde has a three-game goal streak. ... Canucks C Markus Granlund left with an ankle injury and is returning to Vancouver. ... Nilsson is 0-3 against Tampa Bay.
Canucks: Play Friday night at Carolina.
Lightning: Will retire Lecavalier's uniform No. 4 before Saturday night's home game against Los Angeles. He will join St. Louis as the only Tampa Bay players so honored.