Dallas, which will return to the postseason after failing to qualify last season, is one point ahead of the Nashville Predators for the first wild card from the Western Conference. Nashville has one game in hand.
"We're in the playoffs," Stars coach Rick Bowness said. "It's great for the city, it's great for our fans, and it's going to be a great atmosphere here when we get back."
Travis Boyd capped the comeback for the Coyotes when he scored at 1:43 of overtime. Kyle Capobianco's centering pass hit the skate of Jamie Benn, and Boyd quickly shot short side as Scott Wedgewood was moving the other way.
Tyler Seguin had a goal and an assist, Joe Pavelski had two assists, and Wedgewood made 33 saves for the Stars (45-30-6), who will conclude their regular season against the Anaheim Ducks on Friday.
"It's a big point, and a playoff berth is what we were fighting for," Wedgewood said. "It's huge for our organization, our team, all the guys what they've done all year. Since I've been here (acquired in a trade with the Coyotes on March 20) it's been a tough battle. You're obviously upset losing the game when you can get another point in the [wild card] race, but it takes a lot of pressure off Friday for just [staying] alive, which we are now. Just win a game on Friday and see what happens."