Brayden Point had two goals and two assists, and Andrei Vasilevskiy made 23 saves for the Lightning (14-9-2), who have won three of their past four games.
It was the second straight four-point game for Point, who has 12 points (six goals, six assists) in his past five games.
“Just another kind of 'Kuch' night, factoring in on all the goals, so great to have him back,” Point said. “It was a good team effort for us, though, a lot of guys blocking shots, sacrificing, taking hits to make plays and that's why we ended up winning."
Tampa Bay lost two players during the game. Forward Anthony Cirelli left the game after getting hit awkwardly into the bench by Vancouver defenseman Noah Juulsen with 6:11 left in the first period, and defenseman Erik Cernak left after taking a hit from Canucks forward Aatu Raty on his first shift of the third period.
“Tough night, especially we're on the road here for four [games] out west, and to lose some of these guys early on, so we'll know more tomorrow,” Lightning coach Jon Cooper said. “Nervous about these. It's hard right after the game because you don't really know, but let you know [on Monday in Edmonton].”
Quinn Hughes and Kiefer Sherwood scored, and Kevin Lankinen made 29 saves for the Canucks (14-8-4), who lost in regulation for the first time in five games (3-1-1).
Vancouver went 0-for-2 on the power play, including only generating just one shot on an early four-minute advantage after Hughes was high-sticked by Brandon Hagel. Tampa Bay went 2-for-4 on the power play.
“Special teams won the game for them, and their best players,” Canucks coach Rick Tocchet said. “But I thought 5-on-5 we were fine. It’s just obviously unfortunate, can't have that too many men (penalty that led to the winning goal). And then it’s the Kucherov show. There you go. So, that's the way I look at it.”