The Bolts came out flying in the first, racing out to a 4-0 lead. Stamkos hit the milestone at 4:40 of the period and was followed by goals from Nikita Kucherov and Brayden Point before adding a second goal himself.
A pair of Vancouver power play goals in the third tightened things up, but Stamkos completed Tampa Bay's first hat trick of the season with an empty net goal in the final two minutes of regulation to round out the scoring.
Brian Elliott got the start in goal for the Lightning in the first half of the back-to-back and earned the victory with 37 saves.
It's now on to Edmonton for the Bolts, where they'll face the Oilers on Thursday at Rogers Place.
Scoring Summary
1st Period
TBL 1, VAN 0
4:40 Steven Stamkos (19) - Alex Killorn
Steven Stamkos became the 47th member of the NHL's 500 goal club less than five minutes into the first period. Alex Killorn made a nice move around Ilya Mikheyev and dished to a wide-open Stamkos in front of the net for a tap-in goal.
TBL 2, VAN 0
8:28 Nikita Kucherov (18) - Brandon Hagel, Brayden Point
A gap in the middle of the ice opened up for Brandon Hagel to thread a pass through to Nikita Kucherov at the right circle for a one-timer that was blasted past Spencer Martin.
TBL 3, VAN 0
13:18 Brayden Point (26) - Erik Cernak, Ross Colton
Tampa Bay's first period onslaught continued when Brayden Point swept home a rebound on his backhand. Erik Cernak took the initial shot from along the near wall and Martin kicked it directly to Point below the left circle.
TBL 4, VAN 0
14:35 Steven Stamkos (20) - Alex Killorn
Stamkos added his second goal of the period less than two minutes later to put the Bolts up by four headed to intermission. Killorn circled the Vancouver net and fed Stamkos. He cut wide around Martin and tucked the puck around the goaltender's pad. The Canucks would make a goaltender change following the goal, pulling Martin and replacing him with Collin Delia.
2nd Period
No Scoring
3rd Period
TBL 4, VAN 1
6:35 Andrei Kuzmenko (18) - Quinn Hughes, J.T. Miller - PPG
The Canucks got on the board with a power play goal in the opening stages of the third period. Quinn Hughes blasted a shot from the point that was tipped past Brian Elliott by Andrei Kuzmenko in front of the net.
TBL 4, VAN 2
9:10 Quinn Hughes (4) - J.T. Miller, Bo Horvat - PPG
The Bolts suddenly found their lead trimmed to two midway through the third on Vancouver's second power play goal of the period. Hughes got to the front of the net and slipped a backhander past Elliott to make it 4-2.
TBL 5, VAN 2
18:38 Steven Stamkos (21) - Nikita Kucherov - ENG
Stamkos completed the hat trick and put an end to Vancouver's comeback bid with an empty net goal with less than two minutes to play.
