Up 5-2 with less than five minutes to play in regulation, Tampa Bay allowed goals to Quinn Hughes and Elias Pettersson in rapid succession to suddenly find themselves in a one-goal game. Making things more difficult was an Alex Killorn tripping minor that gave the Canucks a 6-on-4 advantage once they managed to pull Collin Delia.
Vasilevskiy held firm, however, making a series of saves down the stretch, highlighted by that point-blank stop on Lazar just as time expired.
With the victory, Tampa Bay's home winning streak sits at nine games.
The Bolts now depart on a five-game Western Conference road trip that begins on Saturday in St. Louis.
Scoring Summary
1st Period
VAN 1, TBL 0
4:14 Conor Garland (8) - Bo Horvat, Luke Schenn
Tampa Bay lost coverage of Bo Horvat and Conor Garland in front of the net, leading to the game-opening goal. Andrei Vasilevskiy made a big pad stop on Horvat's rebound try in tight but kicked the third chance to Garland wide-open at the side of the net. He buried the shot to give Vancouver the lead with Vasilevskiy unable to recover.
VAN 1, TBL 1
14:37 Corey Perry (6) - Mikhail Sergachev, Ross Colton - PPG
In the closing seconds of their first power play chance of the night, the Lightning responded to tie the game at one. Mikhail Sergachev took the initial shot from the right point, and Corey Perry got positioning in front of Collin Delia to tip it home.
2nd Period
TBL 2, VAN 1
2:30 Alex Killorn (13) - Nick Perbix, Brandon Hagel
Nick Perbix's shot from the point was blocked and fell free in the slot. Alex Killorn pounced on the puck with his back to goal, spun and whipped a shot past Delia's glove to give the Lightning their first lead of the night.
TBL 2, VAN 2
5:44 J.T. Miller (16) - Quinn Hughes, Collin Delia - PPG
A Quinn Hughes stretch feed found J.T. Miller at the far blue line to create a breakaway chance. In alone on Vasilevskiy, Miller made a backhand move and tucked the puck around Vasilevskiy's pad for a power play goal.
TBL 3, VAN 2
15:44 Nikita Kucherov (17) - Steven Stamkos, Brayden Point
A Nikita Kucherov shot from the slot got the play started, and hard work in front of the net put Tampa Bay in front again. Delia made the first save and denied Steven Stamkos on the rebound, but Kucherov drove to the net and put home the loose puck.
TBL 4, VAN 2
19:29 Brandon Hagel (16) - Alex Killorn, Nick Perbix
In the final minute of the period, two Canucks skaters followed Killorn into the corner. He still managed to slip a backhand feed back to Brandon Hagel open in front of the net and he one-timed it past Delia for an insurance marker.
3rd Period
TBL 5, VAN 2
5:30 Steven Stamkos (18) - Brayden Point, Nikita Kucherov - PPG
The Lightning cashed in on a lengthy two-man advantage to extend the lead to three. Tampa Bay went with five forwards on the 5-on-3, and Brayden Point teed Stamkos up for a big one-timer from the left circle that marked the 499th goal of his career.
TBL 5, VAN 3
14:40 Quinn Hughes (3) - Elias Pettersson, Andrei Kuzmenko
Quinn Hughes got the Canucks back within two with less than five minutes to play, snapping home a wrist shot from the high slot.
TBL 5, VAN 4
17:52 Elias Pettersson (18) - Quinn Hughes, J.T. Miller
Vancouver made things interesting down the stretch, cutting the Lightning's lead to one with their net empty. Hughes set up Elias Pettersson for a one-timed blast from the top of the right circle that beat Vasilevskiy.