Roope Hintz scored for the Stars (41-27-4), who are 6-2-1 in their past nine games.
Dallas holds the second wild card into the Stanley Cup Playoffs from the Western Conference. The Stars are three points ahead of the Vegas Golden Knights and one point behind the Nashville Predators for the first wild card.
"That was playoff hockey," Stars coach Rick Bowness said. "That's probably the best game of the year. It's a 1-0 game with plenty of scoring chances at both ends, great goaltending. Just great second efforts tonight. You saw guys diving in front of shots and taking hits to make plays; that's what it's all about. We talked to them this morning, it's all-in now. We're all-in, everybody. And we had everybody on it tonight."
Andrei Vasilevskiy made 28 saves for the Lightning (44-21-8), who have one win in their past six games and are 10-10-2 since March 1. Tampa Bay is third in the Atlantic Division, four points behind the Toronto Maple Leafs for second and one point ahead of the Boston Bruins.
"We've given up two goals in the last three games (2-1 overtime loss against the Bruins on Friday, 5-0 win against Buffalo Sabres on Sunday), and we've lost two of them," Lightning captain Steven Stamkos said. "The defensive side has been a lot better, but you also can't win a game when you don't score. It's just about finding that balance now."
Hintz made it 1-0 at 15:10 of the third period off a pass from behind the net by Joe Pavelski. The Stars forward was uncovered in the slot and one-timed the pass for his fourth point (two goals, two assists) in two games.
"There wasn't much time left, and the fans were going crazy," Hintz said. "They were great today. They've been like that every game we've played here. It's so nice to play [at home]."