Valtteri Filppula and Tom Pyatt also scored for the Lightning, who moved into a second-place tie with Montreal—with one game at hand—in the Atlantic Division after completing a 3-1-2 homestand. Ben Bishop extended his single-season team record with his 32nd win.
Vancouver, which started play 10th in the Western Conference, is 3-6-1 in its last 10 games. Alexandre Burrows scored two goals, and Jannik Hansen added a short-handed tally for the Canucks.
After Pyatt scored midway through the third period, the Canucks got within one on goals by Burrows at 11:44 and Hansen at 15:16.
Stamkos put the Lightning up 1-0 with a power-play goal from the low slot 17:56 into the game. Palat assisted on the goal, and has five assists and nine points during a five-game point streak.
Bishop made in-close rebound saves on Alexander Edler and Shawn Matthias late in the first.
After Eddie Lack stopped eight Lightning shots early in the second, Tampa Bay went ahead 2-0 when Palat's pass went off sliding Canucks defenseman Ryan Stanton and into the net at 6:54.
Filppula made it 3-0 with 9 seconds left in the second when his pass deflected off Stanton and past Lack. The center has two goals and eight points during a five-game point streak.
Burrows ended Bishop's bid for a second consecutive shutout on a power-play rebound goal 5:44 into the third. Bishop got his fifth shutout this season in a 3-0 victory over New Jersey on Saturday.
NOTES: The Lightning held a pregame ceremony honoring the 2004 Stanley Cup championship team. Vancouver coach John Tortorella coached Tampa Bay in 2004 and walked to center ice to a loud ovation when he was introduced. ... Stamkos has two goals in six games since he returned from a broken right shin. ... Filppula's goal was his 300th NHL point.