Darren Raddysh had a goal and two assists for the Lightning (15-7-2), who are 14-3-0 in past 17 games after a 1-4-2 start, and Andrei Vasilevskiy made 33 saves for his sixth consecutive win in goal.
Nikita Kucherov had two assists to extend his point streak to eight games (15 points; four goals, 11 assists). Gage Goncalves, Jake Guentzel and Brandon Hagel also scored for Tampa Bay.
J.T. Compher and Michael Rasmussen each had a goal and an assist and Dylan Larkin scored for the Red Wings (13-11-1), who have lost three straight and four of five (1-4-0) after going 3-0-1 in their previous four games. John Gibson made 22 saves.
Detroit took a 1-0 lead at 8:29 of the first period when Compher put in Rasmussen’s pass from the corner for his fourth goal of the season.
The Lightning made it 1-1 with a power-play goal at 17:07. Kucherov’s pass found Raddysh alone in the high slot and his slap shot through traffic beat Gibson.
Tampa Bay took a 2-1 lead at the 34-second mark of the second period when Goncalves beat Albert Johansson to a loose puck in the slot and put it past Gibson for his second goal of the season.
Gourde made it 3-1 at 3:01, chipping a rebound over Gibson, but Rasmussen took just 12 seconds to cut the margin to 3-2, tapping a rebound over the goal line for his third goal of the season at 3:13.
Gourde restored Tampa Bay’s two-goal lead at 16:09, firing a shot through traffic to make it 4-2, but Larkin cut the deficit to 4-3 at 18:26, putting a wrist shot from a sharp angle past Vasilevskiy from the left face-off circle.
It was the second goal of the game for Gourde, who had scored three in his first 23 games this season.
Guentzel made it 5-3 at 12:47 of the third period, tipping in Raddysh’s point shot with the teams playing at 4-on-4.
Hagel scored with Gibson pulled for an extra skater at 17:13 to make it 6-3.