The Lightning (29-13-1) also beat the Canucks 5-4 in Tampa last week.
Vancouver has not won in regulation since a 4-2 victory over Colorado on Jan. 5. The Canucks are 2-8-0 in their last 10 games.
Stamkos sent his third goal of the night — and 21st of the season — into the empty net with 1:22 left.
Hughes cut the Lightning lead to 4-2 after Stamkos was called for tripping midway through the third period.
The defenseman muscled his way to the front of the net and forced a backhanded shot up and over Elliott for his fourth goal of the season at the 9:10 mark.
Tampa Bay grabbed control with four goals in the first period.
Stamkos, who turns 33 on Feb. 7, got his milestone goal at 4:40. Killorn sliced a pass across the low slot to Stamkos, and the Lightning captain tapped it in.
Tampa Bay’s bench emptied, with players mobbing Stamkos in the corner in celebration as the crowd cheered.
“It’s such a humbling experience when you have a moment like that and you get to celebrate it with your teammates, who are genuinely just as excited as you are. I’m so thankful for them,” Stamkos said. “Obviously this is an individual statistic, but it takes so many different players along the way that have helped me get to that.”
After the game, he spoke in the locker room and thanked his teammates for their help and support.
That was the moment that made Tampa coach Jon Cooper the most proud.
“I’ve just watched that kid grow into a man, a phenomenal leader, and to be honest, he’s a generational goal scorer,” Cooper said. “That’s what he is and those guys don’t come around that often. Enjoy him while you can and I’ve been extremely fortunate to enjoy him put that puck in the net hundreds of times. And it’s good for him, well deserved.”
Kucherov scored his 18th goal of the season on a blistering one-timer from a faceoff circle at 8:28. Point’s backhanded shot at 13:18 made it 3-0. It was Point's team-leading 26th of the season.
Stamkos put away his second goal of the night at 14:35, wrapping a wrist shot around Martin’s outstretched pad.
“He’s first class, a first-ballot Hall of Famer, for sure. He scores goals,” said Canucks defenseman Luke Schenn, who played two seasons with Stamkos in Tampa.
Vancouver paid tribute to former Canuck Wayne “Gino” Odjick, who died Sunday at 52. Players wore jerseys with Odjick’s name and No. 29 on the back for warmups. Cheers of “Gino! Gino! Gino!” echoed throughout the rink several times and highlights of Odjick’s career played on the big screen throughout the game.
Stamkos extended his point streak to six games. He has four goals and six assists in the stretch.
Lightning: At Edmonton on Thursday night.
Canucks: Host Colorado on Friday night.
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