Christopher Gibson, in his second start of the season, made 22 saves for his first NHL win since a 4-1 victory for the New York Islanders against the Pittsburgh Penguins on March 20, 2018.
"This has been a long time coming, so it is exciting, for sure," Gibson said. "The guys played great in front of me, so all the credit goes to them."
Filip Zadina scored, and Jonathan Bernier made 40 saves for the Red Wings (18-27-9), who have scored three goals in their past five games and have gone 10 straight games without a power-play goal (0-for-21).
"We've had too many games like this, where the goaltending is good, but we don't score," Detroit coach Jeff Blashill said. "Tonight, [Bernier] was very good, but the power play didn't score when we needed them to get us something."
After being shut out Saturday, the Lightning needed 16 seconds to take a 1-0 lead when Coleman scored off a pass from Barclay Goodrow. It was Coleman's third goal in four games and fifth in the past six.
"We turned the puck over really early, and then we chased [Goodrow] behind the net and left [Coleman] wide open in front," Blashill said. "We can't make that kind of mistake."
Mikhail Sergachev put the Lightning up 2-0 at 1:09 of the second period, sliding a point shot through traffic for his third goal of the season and first in 27 games.
Zadina cut it to 2-1 at 13:37, finishing off a 4-on-2 break by slapping home Vladislav Namestnikov's pass. It was the first goal allowed by Tampa Bay in 164:45, dating to the third period of a 7-4 win against the Chicago Blackhawks on Tuesday.