Ross Colton and Brayden Point scored for the Lightning (26-9-2), who have won two straight since a season-high three-game losing streak.
"We got a good push and I think that's why we got the W tonight," Tampa Bay forward Pat Maroon said. "We were on them quick and got rewarded fast. In the second we kind of stalled there. We played with the lead, and you've got to find ways to move forward when you've got the lead. … We had some people feeling the puck tonight, so it was good to see."
Adam Erne scored, and Thomas Greiss made 27 saves for the Red Wings (12-22-5), who have lost 17 straight regular-season games at Tampa Bay dating to Dec. 12, 2013.
"Not too satisfied right now … we lost 2-1," Detroit captain Dylan Larkin said. "We were there. We didn't have the best start, but we battled back in the game. Vasilevskiy was good. He did what he does. Nothing to be satisfied about, though.
"Just came up short. We can't keep coming up short in games like this against teams like that. We've got to start getting results. It's not going to be easy, but we can't be satisfied with a 2-1 loss."
Colton gave the Lightning a 1-0 lead at 4:07 of the first period when he chipped the puck past a sprawling Greiss on a rebound.
"Guys did a good job of blocking shots and [Vasilevskiy] made some big-time saves for us obviously, as usual," Tampa Bay defenseman Victor Hedman said. "It was a hard game. [Detroit] has been playing some really good hockey as of late, so we knew it was going to be a battle. Very happy to come out on top."
Point made it 2-0 at 7:26 of the first, receiving a pass from Hedman near the right post and beating Greiss over his glove.
"We came out really strong in the first period," Lightning coach Jon Cooper said. "You get a 2-0 lead, we should be able to shut that down and for the most part we did. But we gave up too many chances in the third. Some were unlucky breaks, but for the most part we were just a little too loose. Part of it is that we were pressing for a third goal and we couldn't get it, and it was opening us up a little bit."