Jamie Benn and Alexander Radulov scored 41 seconds apart in the third period to tie the game for the Stars (9-9-7). Jake Oettinger made 33 saves.
"Great point. Any points you can get when you're chasing a playoff position is important," Dallas coach Rick Bowness said. "Especially after that first period, which was probably our worst period of the year. We battled back. We didn't quit. There's a lot of fight in this hockey club."
Victor Hedman had an assist for his 500th NHL point, and Brayden Point had a goal and an assist for the Lightning (20-6-2), who have won all three games against the Stars this season. Andrei Vasilevskiy made 24 saves for his ninth straight win since Feb. 22.
Hedman leads all NHL defensemen this season with 27 points (five goals, 22 assists) in 28 games. The No. 2 pick by Tampa Bay at the 2009 NHL Draft, he has 110 goals and 390 assists in 790 games and is the first defenseman to score 500 points for the Lightning.
"[500 points] means the world," Hedman said. "This has been my home for a long time and there's nowhere else I want to be. I want to keep winning. To reach milestones is always fun. That's a big milestone and hopefully some more to come."
The Stars scored twice with Oettinger pulled for an extra attacker. Benn made it 3-2 at 17:54 of the third period on a redirection, and Radulov tied it 3-3 at 18:35 when Benn's pass from behind the net went off his leg in front and past Vasilevskiy.
Ross Colton and Point scored in the shootout for Tampa Bay. Jason Robertson scored for Dallas.
"We're happy we got a point, [but] I wish we would've got two," Benn said. "We're never out of the game; just a group of guys that don't quit. Obviously we don't want to be coming back too much down the stretch, but it's nice to see we still got some fight."