Tyler Seguin extended the lead to 2-0 at 16:49, skating around Larkin and down the left wing before cutting to the slot and scoring his first goal of the season.
"I didn't think much happened in the first period either way, but [Larkin's] line made two mistakes and we were down 2-0," Red Wings coach Jeff Blashill said. "They weren't good in that period, but they really stepped up for the last two."
Mantha cut it to 2-1 with a power-play goal 48 seconds into the second period.
"I didn't actually mind our power play (which went 1-for-8)," Blashill said. "We got some chances, and even if we didn't score, that's a lot of time we're running off the clock where they aren't getting a chance to create offense."
Mantha tied it 2-2 at 9:43 after skating around Stars defenseman Esa Lindell and cutting across the crease before finishing into an open net. He completed the hat trick 15 seconds into the third period, tapping in a rebound from the edge of the crease to make it 3-2.