"I didn't like our dig level at all," Red Wings coach Jeff Blashill said. "They are a good defensive team, but we didn't make this game nearly hard enough on them."
Dylan Larkin had two assists, giving him 200 NHL points, and Jonathan Bernier made 32 saves for Detroit.
The Red Wings nearly scored first midway through the first period when Darren Helm took the puck away from Dubnyk on a Minnesota power play, but Mikael Granlund stopped the shot on the goal line.
"(Dubnyk) was thanking Granlund after that save," Suter said.
Kunin made it 1-0 for the Wild at 16:56 of the first, putting a rebound in off the goal post for his fifth goal.
"We've got a few young guys who are getting a great chance to play in key situations," Kunin said. "We know we need to take advantage of it, and I felt like we did that tonight. It's big to be getting time on the power play and being on the ice when we've got a one-goal lead in the last two minutes."
Jordan Greenway gave Minnesota a 2-0 lead at 18:54, skating past Anthony Mantha and scoring his 11th goal.
"I had a pretty good look on that one," Greenway said. "If I had missed it, I don't think I would have slept much tonight."