It's the 13th time Stamkos has scored 20 goals in a season, passing Vincent Lecavalier for the most in Lightning history.
"The thing that made me probably the most proud is what he said to the team after the game, and how he thanked everybody," Cooper said of Stamkos. "I've watched that kid grow into a man, a phenomenal leader, and to be honest, he's a generational goal scorer. That's what he is, and those guys don't come around that often. Enjoy him while you can. I've been extremely fortunate to enjoy him put that puck in the net hundreds of times. Good for him, well deserved."
Martin was pulled after allowing four goals on 10 shots and replaced by Collin Delia, who made 14 saves in relief.
Andrei Kuzmenko deflected a Hughes point shot on the power play to cut it to 4-1 at 6:35 of the third period, and Hughes scored on a solo rush on another power play at 9:10, finishing with a backhand deke in tight to make it 4-2.
"I think we were angry," Boudreau said of the difference after the first period. "And I think we're a non-quitting team, win or lose."
Stamkos completed his 11th NHL hat trick into an empty net at 18:38 for the 5-2 final. After receiving a standing ovation from the Vancouver crowd for his 500th goal, Stamkos wasn't surprised to see the ice littered with hats after his third.
"The thing that's going to stick out too is obviously the goal, but just the reception I got from the crowd," Stamkos said. "That's something as a player that sticks with you for a long time when you're on the road and you get that type of reception."
NOTES: Stamkos extended his point streak to six games and 10 points (four goals, six assists). Killorn has six points (two goals, four assists) on a four-game point streak, and Hagel has seven points (two goals, five assists) on a five-game point streak. … Hughes has nine points (three goals, six assists) during a five-game point streak. … Horvat had an assist to extend his NHL career-long point streak to nine games (10 points; four goals, six assists). … Vancouver is 5-15-1 against teams from the Eastern Conference this season. Tampa Bay is 14-4-4 against the Western Conference.