Tampa Bay staked themselves to a 3-0 lead 8:04 into the contest on the back of two Brayden Point goals and another from Alex Killorn.
St. Louis briefly made it a one-goal game early in the second period, but Brandon Hagel scored an insurance marker just 18 seconds later to quickly put the Bolts back in front by two.
Nick Paul added the lone goal of the third period into an empty Blues net put the game out of reach and round out the scoring.
The Bolts now depart on a three-game road trip to the Northeast that begins with back-to-back Atlantic Division games against Buffalo and Boston.
Scoring Summary
1st Period
TBL 1, STL 0
3:29 Brayden Point (7) - Brandon Hagel, Nikita Kucherov
Unable to get his stick free, Brandon Hagel fought through a check at the side of the net and kicked the puck over to Brayden Point in the slot. Point dragged the puck around Colton Parayko to his backhand and swept home the shot to give the Bolts the lead.
TBL 2, STL 0
3:57 Alex Killorn (7) - Nick Paul, Steven Stamkos
Less than 30 seconds later, the Lightning doubled their advantage on a one-timer from Alex Killorn just inside the right circle. Nick Paul set things up, forcing a turnover and then making the pass to Killorn from his knees on the left wing.
TBL 3, STL 0
8:04 Brayden Point (8) - Nikita Kucherov, Mikhail Sergachev - PPG
Tampa Bay's fast start continued when Point recorded a power play goal at 8:04 for his second tally of the period. Point took a feed from Nikita Kucherov in the slot, turned to goal and ripped a shot past Jordan Binnington to make it 3-0.
TBL 3, STL 1
16:50 Pavel Buchnevich (6) - Robert Thomas, Jordan Kyrou - PPG
The Blues used their first power play of the game to get on the board late in the first period. Pavel Buchnevich set up next to Andrei Vasilevskiy and redirected a feed from Robert Thomas home at the side of the net.
2nd Period
TBL 3, STL 2
6:24 Jordan Kyrou (7) - Robert Thomas, Pavel Buchnevich
Thomas pulled up at left circle and found Jordan Kyrou trailing on the rush. Kyrou skated to the slot and snapped his shot past Vasilevskiy to get the Blues back within a goal.
TBL 4, STL 2
6:42 Brandon Hagel (6) - Nikita Kucherov, Brayden Point
Tampa Bay had a quick response and went back up by two, 18 seconds later. From along the far wall, Kucherov fed Hagel in the slot. Binnington got a piece of the ensuing shot with his glove but not enough to keep it out of the net.
3rd Period
TBL 5, STL 2
16:12 Nick Paul (9) - Alex Killorn, Steven Stamkos - ENG
The Blues pulled Binnington in exchange for a sixth skater coming out of the final media timeout of the third, but Nick Paul quickly made them pay with an empty net goal.
