Joe Pavelski had a goal and two assists, and Braden Holtby made 39 saves for the Stars (11-7-2), who have outscored opponents 18-6 during the streak.
Hintz has seven goals in his past five games and 10 in the past nine.
"Right now, it's going in," Hintz said. "I'm getting good passes from my linemates (Pavelski, Jason Robertson) and teammates, so that helps."
Jesperi Kotkaniemi scored, and Frederik Andersen made 13 saves for the Hurricanes (15-5-1), who have lost their past two games and four of five (1-3-1).
"Ideally, we'd never lose two games in a row," Carolina defenseman Ian Cole said. "Maybe that's a bit of a pipe dream, but that's the goal. I think the foundational mindset behind that is, 'Hey, let's right the ship right away, let's not let this linger. Let's continue to play well,' but hey, we lost. That's not good enough.
"The name of the game as a professional athlete is to win. That's it. That should be our only focus. We played well today, we had a lot of shots, we had a lot of Grade A [chances]. We should have scored more goals, you know, X, Y, and Z, but we lost. So really, that's all that matters. We need to figure out ways to win, and we need to figure them out quick. We can't let this continue to slide, it's only going to hurt us in the long run."
Dallas scored within the first two minutes for the third straight game when Hintz collected the rebound of his own shot and put it top shelf to make it 1-0 at 1:13 of the first period.