Tyler Seguin scored off a Jamie Benn pass from below the goal line to give Dallas a 5-4 lead with 7:32 remaining after Arizona scored two straight goals in 1:01 to tie the game.
Roope Hintz
, John Klingberg, Radek Faksa and Mattias Janmark scored for the Stars (28-21-4), who had not won five in a row since Feb. 1-9, 2018. Benn and Miro Heiskanen each had two assists, and Ben Bishop made 38 saves.
"It's believing in the system, getting confidence and going into third periods finding ways to win hockey games in all kinds of different ways," Benn said.
WATCH: [All Coyotes vs. Stars highlights]
Oliver Ekman-Larsson, Kevin Connauton, Vinnie Hinostroza and Alex Galchenyuk scored for the Coyotes (23-24-5), who have lost three straight games. Clayton Keller and Nick Cousins each had two assists, and Darcy Kuemper made 24 saves.
"We worked hard and competed and did our best to give ourselves a chance to win the game," Arizona forward Lawson Crouse said. "But at the end of the day, they got that clutch goal there at the end that determined the outcome."
Ekman-Larsson gave the Coyotes a 1-0 lead at 8:39 of the first period with a wrist shot from the left face-off circle, converting a cross-ice pass from Cousins on a 3-on-2 rush.
It was Ekman-Larsson's 109th NHL goal, passing Teppo Numminen for most by a defenseman in Coyotes/Winnipeg Jets history.
"You'd rather win the hockey game than breaking records," Ekman-Larsson said. "It means a lot to me, that I've been able to score a lot of goals for this organization, and hopefully I have a lot more in me."