After a strong start, Tampa Bay's play dipped in the second period, with Detroit scoring three goals in less than four minutes to take a 3-2 lead into intermission.
Ross Colton scored his second goal of the game in the opening minute of the third period, but Jakub Vrana answered on a breakaway five minutes later for the game-winning tally.
Steven Stamkos assisted on all three Lightning goals to reach 953 career points and tie Martin St. Louis' record for the most in franchise history.
The Bolts will return to AMALIE Arena on Thursday to face the Maple Leafs at 8 p.m.
Scoring Summary
1st Period
No Scoring
2nd Period
TBL 1, DET 0
3:58 Ross Colton (18) - Steven Stamkos, Ondrej Palat
After a scoreless opening 20 minutes, play opened up in the middle frame with Tampa Bay getting on the board first. Steven Stamkos sliced his way through the middle of the Detroit defense and appeared to be in alone on Thomas Greiss. The goaltender played Stamkos to shoot, but he instead dished to Ross Colton on the left, who had a wide open net to aim for with Greiss pulled out of position.
TBL 1, DET 1
4:20 Oskar Sundqvist (7) - Danny DeKeyser, Moritz Seider
Tampa Bay's lead lasted all of 22 seconds before the Red Wings equalized. Andrei Vasilevskiy made the save on Danny DeKeyser's shot from the point, but before he could cover, Oskar Sundqvist swept home the rebound on his backhand to level the game at one.
DET 2, TBL 1
6:34 Jakub Vrana (11) - Filip Zadina, Jake Walman
Just as a Detroit power play expired, Jakub Vrana gave the Red Wings the lead with a shot from inside the right circle that got through traffic and past Vasilevskiy
DET 3, TBL 1
8:17 Lucas Raymond (23) - Unassisted
Lucas Raymond stripped Mikhail Sergachev of the puck in the neutral zone and skated down the right wing to the circle. Raymond's shot beat Vasilevskiy to cap a stretch of three Red Wings goals in less than four minutes.
DET 3, TBL 2
9:47 Nikita Kucherov (19) - Victor Hedman, Steven Stamkos - PPG
With momentum firmly on Detroit's side, Jon Cooper used his timeout following Raymond's goal to try and settle his team. The move paid off with the Bolts quickly pulling back within one courtesy of a Nikita Kucherov power play goal. Tampa Bay won the opening face-off of the power play and worked the puck to Kucherov along the far wall. Kucherov drifted down below the right dot and slipped a shot through Greiss' five-hole.
3rd Period
DET 3, TBL 3
0:43 Ross Colton (19) - Steven Stamkos, Erik Cernak
Colton's second goal of the night tied the game at three in the opening minute of the third. From the corner, Stamkos spotted Colton open in the slot and set him up for a one-timer that was blasted past Greiss. With the assist, Stamkos collected career point No. 953, matching Martin St. Louis' record for the most in franchise history.
DET 4, TBL 3
5:09 Jakub Vrana (12) - Unassisted
The Lightning won an offensive zone draw, but Sergachev had the puck poked free by Vrana just inside the blue line. Vrana had a breakaway from the red line in and snapped a shot past Vasilevskiy to put Detroit back in front for good.
