Brunnstrom scored three goals in his first NHL game to match the league record, Mike Modano had two goals and the Stars beat the Nashville Predators 6-4 on Wednesday for Dallas' first victory of the season.
The Stars outbid several NHL teams in May to sign the skilled Swedish left wing, but Brunnstrom was a healthy scratch in Dallas' first two games.
Brunnstrom insisted he wasn't upset at the snub and proved it, breaking a 4-4 tie with 3:25 left when he struck from close range off a feed from Brad Richards.
The Swede became the third player in NHL history to score a hat trick in his first game, joining Alex Smart of the Montreal Canadiens (Jan. 14, 1943) and Real Cloutier of the Quebec Nordiques (Oct. 10, 1979).
"I wanted to play and be part of the team, but this team has really good players so you have to earn your spot," Brunnstrom said. "I felt comfortable out there from the start. It was fun, but the most important thing was that we won the game."
Brunnstrom gave Dallas a 4-3 advantage at 14:13 of the second period after Ryan Jones' first career goal 23 seconds earlier had drawn the Predators even.
Playing on a line with Richards at center and Sean Avery on the right side, Brunnstrom scored from the slot for his first career goal at 11:45 of the second period for a 3-2 lead.
"He was nervous when he got here," Richards said. "There's a lot of expectations on him and it was unreasonable. We wish he could have a hat trick every night but he was in the right place at the right time."
Stars coach Dave Tippett said that while the goals were nice, he also liked the rookie's all-around game.
"He's doing things beyond the goals that make you feel good," Tippett said. "He's a good player who will continue to improve."
Modano's empty-netter -- the 530th goal of his career -- sealed the win with 3.3 seconds left.
Martin Erat tied it at 4 for Nashville with 9:01 left in the third period on a goal upheld on video review. Marty Turco stopped Erat's rebound attempt, but replays showed the puck was over the goal line when Turco controlled it.
Stephane Robidas added a power-play goal for Dallas (1-1-1).
"I played against him lots of times," Hornqvist said. "I know he's a good player. We need to stay tight to him."
The Predators were playing their fourth game in six nights, but they rallied three times to extend the Stars.
"It's disappointing," Nashville coach Barry Trotz said. "I didn't think we played a particularly great game, but we found a way to come back. When we get four goals, we've got to get a point in the hockey game. We were short in coverage on a number of their goals."
Robidas gave the Stars the lead when his one-timer glanced off the stick of a Nashville player and past goalie Dan Ellis with 10 seconds left in the opening period.
Modano, the NHL goal-scoring leader among U.S.-born players, made it 2-0 29 seconds into the second period, converting B.J. Crombeen's centering pass.
Bonk's power-play goal on a re-direct cut it to 2-1 at 3:56 of the second period.
Hornqvist tied it at 2 when his shot from the point glanced off the stick of Robidas and through the pads of Turco at 9:04 of the second period.
- Nashville C Jason Arnott missed the first of an anticipated three games because of a fractured finger on his right hand.
- The Predators beat the Stars 3-1 on Saturday night in Nashville, outshooting Dallas 32-20.
- Loui Eriksson's apparent power-play goal for Dallas was disallowed at 6:56 of the first period because teammate Brenden Morrow had been whistled for goalie interference.