Alex DeBrincat and Dylan Larkin each had a goal and an assist for the Red Wings (24-18-5), who went 3-for-4 on the power play and were 7-1-1 in their previous nine games.
Alex Lyon allowed five goals on 32 shots before being pulled after the second. James Reimer made six saves in the third period.
“We’ve been playing well and focusing on the details,” DeBrincat said. "Twenty minutes cost us the game. We played well in the third too. We’ll learn from this.”
Jason Robertson gave Dallas a 1-0 lead with a power-play goal at 3:24 of the first period.
David Perron tied it 1-1 at 14:33 with one second left on a power play, and DeBrincat made it 2-1 at 16:53, just as another man-advantage was about to expire.
Mason Marchment started the four-goal outburst for the Stars when he tied it 2-2 just 22 seconds into the second with a shot from the left circle.
Hintz gave Dallas a 3-2 lead at 4:35, stealing the puck at the edge of the crease and scoring his 21st goal.
Esa Lindell made it 4-2 on a rebound at 11:40, and Hintz scored his second of the period at 15:12 after Johnston stole the puck inside the Red Wings’ blue line to push the lead to 5-2.
“I think Wyatt was probably our best player tonight,” Stars coach Pete DeBoer said. “He was outstanding, but his whole line (with Robertson and Hintz) was really good.”