Erik Cernak had a goal and two assists, and Andrei Vasilevskiy made 20 saves in his 300th game for the Lightning (36-14-3), who extended their point streak to seven games (6-0-1).
"We're playing pretty decent defensively," Tampa Bay coach Jon Cooper said. "When you're playing the same teams over and over again and they are all defensive and have pretty good structure in their defensive games, you've got to be on your game in that regard, and it's probably helped us."
Tyler Seguin and Andrej Sekera scored, and Jake Oettinger made 14 saves for the Stars (21-18-14), who are 0-3-2 in their past five games.
Dallas remained four points behind the fourth-place Nashville Predators with a game in hand for the final Stanley Cup Playoff berth from the eight-team division. The Predators lost to the Columbus Blue Jackets 4-2 on Wednesday.
The Lightning moved into a tie for second place with the Florida Panthers, four points behind the first-place Carolina Hurricanes. All three have clinched a playoff berth.
"I mean, we understand we need to win, and we need help," Stars forward Joe Pavelski said. "We have to win our next game (Friday at Tampa Bay) and focus from there and see what happens. That's the biggest thing. We have to have a narrow focus, have to win a game and go from there. We're not going to get all three at once, so focus on the first one."
Tyler Johnson gave the Lightning a 1-0 lead at 2:14 of the first period when he finished a rush that started when Alex Killorn forced a turnover. It was Johnson's first goal in 22 games.
"You have to be comfortable in [low-scoring, tight-checking] games," Johnson said. "That's how you win championships. We were very good at it last year and hopefully we're learning this year and getting better at it."