With the loss, Tampa Bay wraps up the road trip with a 2-1-1 record.
Twice the Bolts led by a goal in the opening period, but each time Vegas came back to tie it up, eventually going ahead for good on Shea Theodore's goal at 14:20 of the first frame.
Andrei Vasilevskiy gets saddled with the loss after making 21 saves on 25 shots.
Tampa Bay now returns home to open a brief two-game homestand on Tuesday against the Ducks.
Scoring Summary
First Period
TBL 1, VGK 0
6:10 Vladislav Namestnikov (6) - Corey Perry, Mikhail Sergachev
From along the near wall, Corey Perry threw the puck toward the front of the net. Vladislav Namestnikov had his stick on the ice to redirect the feed upstairs on Adin Hill for game-opening tally.
TBL 1, VGK 1
6:17 Brett Howden (3) - Keegan Kolesar, Alex Pietrangelo
The Lightning's lead lasted just seven seconds before Brett Howden tied things up. Off the ensuing faceoff following the Namestnikov goal, Keegan Kolesar tried to center for Howden streaking toward the net. Andrei Vasilevskiy tried to poke the feed away, but the puck snuck through, and Howden tapped it over the line on his backhand.
TBL 2, VGK 1
6:57 Steven Stamkos (25) - Victor Hedman, Nikita Kucherov - PPG
Just six seconds into Tampa Bay's first power play of the night, Victor Hedman teed up Steven Stamkos for a one-timed blast from the left circle that beat Hill.
TBL 2, VGK 2
8:17 Jonathan Marchessault (16) - Paul Cotter, Shea Theodore
Again Vegas had a quick response, tying the game once more when Jonathan Marchessault picked out the top corner on Vasilevskiy with a wrist shot from just inside the left circle.
VGK 3, TBL 2
14:20 Shea Theodore (6) - Reilly Smith, William Karlsson
Shea Theodore's one-timer from the slot barely trickled through Vasilevskiy's body and over the line to give Vegas their first lead of the game.
VGK 4, TBL 2
17:46 Jonathan Marchessault (17) - Shea Theodore, Reilly Smith
Marchessault knocked down Theodore's shot in front of the net and put home the loose puck at the near post to extend Vegas' lead. Tampa Bay challenged the goal, arguing Marchessault had initially made contact with a high stick, but the call on the ice stood.
2nd Period
VGK 4, TBL 3
4:29 Corey Perry (11) - Victor Hedman
Victor Hedman stepped up to intercept a pass just inside the blue line and poked it ahead for Perry. Hill got a big piece of Perry's wrist shot with his glove, but the puck still got through.
3rd Period
VGK 5, TBL 3
18:51 Nicolas Roy (11) - Unassisted - ENG
With Vasilevskiy pulled for the extra attacker, Nicolas Roy intercepted a pass and hit the empty net from his own zone.
VGK 5, TBL 4
19:49 Pierre-Edouard Bellemare (4) - Mikhail Sergachev, Vladislav Namestnikov
Pierre-Edouard Bellemare gave Tampa Bay a glimmer of hope with 11 seconds to play in regulation when he cut the deficit to one with a redirection. Vegas would manage to kill the final seconds of the third to preserve the win.
