Jagr delivered the game-deciding goal in the fourth round of the shootout as the Stars snapped a four-game losing streak by beating the Phoenix Coyotes 4-3 before 18,181 at American Airlines Center.
Jagr, who was just 5-for-23 in the tiebreaker before Friday, ripped a wrist shot that hit the bottom of goaltender Mike Smith's glove, rolled over his pad and trickled over the goal line to give the Stars the win.
"I think it's pretty exciting for the fans," Dallas coach Glen Gulutzan said. "The fans, seeing Number 68, a guy of that caliber, I think they got their money's worth."
The Stars (3-4-1) begin a three-game trip in Phoenix on Saturday and couldn't afford a home loss.
"Yeah, it was big," Gulutzan said of the win. "First of all, it's a division rival and we've got them tomorrow night too. I think the win itself was best for our psyche and our confidence. It gives us something to try to build off of."
Smith, returning after missing four games with a lower-body injury, stopped 21 of 24 shots. Dallas goaltender Kari Lehtonen made 31 saves.
"He was a good player for us tonight," Phoenix coach Dave Tippett said. "He was a guy that was questionable whether he'd be in the lineup or not. He gave us a heck of a game."
The three goals in regulation were a bonanza for the Stars, who had scored just nine times in their last six games.
"I think there's still room for improvement offensively, as far as putting more shots on net and creating more zone time," said Gulutzan, whose club has been outshot in every game this season. "We're still looking for some chemistry early in the season, and I think that will help our offense."
The Stars led 2-0 in the first period thanks to the first NHL goals by Antoine Roussel, who was making his NHL debut, and rookie defenseman Brenden Dillon. Roussel, the eighth player in NHL history to be born in France, was the first Star to score in his league debut since Raymond Sawada did so against Edmonton on Feb. 9, 2009.
"Obviously, that was fun. I'm happy to get the first one out of the way. Getting a win was most important. Plus I got a goal. That's fun," Roussel said.
Phoenix got one back at 14:00 when Radim Vrbata knocked a 12-foot tip-in off the stick of Dallas center Jamie Benn to make it 2-1. It was Vrbata's third of the season and came after he redirected a shot by Ekman-Larsson from the point
The Coyotes drew the first power play of the night when Dallas defenseman Jordie Benn was whistled for holding David Moss 1:16 before the first intermission. Phoenix tied the game one second after the power play ended when Hanzal beat Lehtonen with a short backhander 45 seconds into the second period. Lehtonen had denied Ekman-Larsson's initial effort, but Hanzal was waiting to pounce at the far post.
At 13:53, things got heated between these Pacific Division rivals. After Dillon delivered a blow to Ekman-Larsson's face near the Stars blue line, he and Phoenix's Kyle Chipchura dropped the gloves behind the Dallas goal, earning 24 total penalty minutes for their confrontation.
Just 21 seconds after that scrum, Michael Ryder put Dallas back in front by beating Smith on the short side with a wrister from the top of the left circle. It was the 400th point of Ryder's career.
Hanzal tied it again with 1:34 remaining before the intermission, beating Lehtonen to the far side with a long wrist shot.
After a scoreless overtime and shootout, Vrbata gave the Coyotes the lead in the shootout by scoring to start the second round. Jamie Benn tied it in the third round before Jagr won it.
Stars rookie defenseman Jamie Oleksiak, the 14th player taken in the 2011 NHL Draft, saw 17:31 of ice time in his NHL debut.
"I thought he played a pretty solid game. I thought he did a good job blocking shots in front of our net and getting people out of the way," Gulutzan said. "I thought it was a good first game for a young guy."
The teams meet again Saturday in Glendale as Phoenix starts a three-game homestand.
"We'll take that point, put it in the bank but we go home tomorrow. On home ice, we need two points tomorrow," Tippett said.