Jake Guentzel had a goal and an assist, and Brayden Point had two assists for the Lightning (6-2-0), who are 5-0-0 at home this season. Dennis Hildeby made 12 saves,
Linus Karlsson and Elias Petterson scored for the Canucks (2-7-1), who have lost seven straight (0-6-1). Kevin Lankinen made 31 saves
Karlsson gave Vancouver a 1-0 lead at 15:32 of the first period, scoring on a slap shot from the top of the right circle.
Petterson's power-play goal at 4:35 of the second period extended the Canucks lead to 2-0. After Hildeby turned away a one-timer from Jonathan Lekkerimaki, Petterson gathered the puck and scored on a sharp angle shot from the goal line.
Kucherov got Tampa Bay on the board with a power-play goal at 6:30 to make it 2-1, scoring on a follow up shot from the right circle after Lankinen saved his initial shot.
Kucherov tied it 2-2 at 11:23 with a snap shot from the left side off of a face-off win from Point.
Guentzel gave the Lightning a 3-2 lead at 2:04 when he scored on a shot from the point that deflected off of Canucks forward Liam Ohgren's stick and caught Lankinen out of position.
Pontus Holmberg pushed the lead to 4-2 at 15:57 when he took the puck off of Zemgus Girgensons' offensive zone face-off win and skated in front of the goal, scoring on a shot below the hash marks.