The win is Tampa Bay's third-straight and gives them a regular season sweep of the Blues.
Andrei Vasilevskiy got the start in net and earned the victory with 23 saves.
The Lightning's five-game trip now heads further west, where they'll face the Kraken in Seattle on Monday evening.
Scoring Summary
1st Period
STL 1, TBL 0
2:39 Tyler Pitlick (2) - Alexey Toropchenko
A feed from Alexey Toropchenko found Tyler Pitlick splitting between Mikhail Sergachev and Nick Perbix. In alone on the breakaway, Pitlick slipped his shot underneath Andrei Vasilevskiy's pad to stake St. Louis to an early lead.
STL 1, TBL 1
12:22 Brayden Point (24) - Nick Perbix
Nick Perbix pinched down from the point and intercepted the puck along the far wall. With the Blues out of position, Brayden Point was left wide-open in the slot and one-timed home Perbix's feed.
TBL 2, STL 1
16:43 Brayden Point (25) - Steven Stamkos, Nikita Kucherov - PPG
Point's second goal of the period gave Tampa Bay the lead just before intermission. On their first power play of the night, Nikita Kucherov won the puck behind the Blues net and set up Steven Stamkos at the left circle. Stamkos then found Point open at the backdoor for a tap-in goal.
2nd Period
TBL 3, STL 1
12:44 Nick Perbix (4) - Mikhail Sergachev, Brayden Point
A soft goal extended Tampa Bay's lead to two. Nick Perbix's shot from the right point went in and out of Jordan Binnington's glove before trickling over the line for his fourth goal of the season.
TBL 3, STL 2
13:55 Pavel Buchnevich (15) - Jordan Kyrou, Robert Thomas
On the rush, Jordan Kyrou found Pavel Buchnevich trailing and worked him the puck. Buchnevich snapped a shot past Vasilevskiy's glove to make it a one-goal game.
TBL 4, STL 2
18:22 Alex Killorn (14) - Brandon Hagel
With Nick Leddy on his tail behind the St. Louis net, Brandon Hagel was able to slip a backhand feed to Alex Killorn at the near post to score and grow the lead to 4-2 late in the second period.
3rd Period
No Scoring
