Mantha scored on a 5-on-3 power play at 14:40 of the second period by tapping in Frk's rebound from the edge of the crease.
"We know when Marty gets the puck on the net, it is either going in or we're going to get a great rebound," Red Wings coach Jeff Blashill said. "Those are both situations we're happy to take."
Dylan Larkin gave Detroit a 2-0 lead at 15:03, beating Dubnyk with a tip of Green's shot on the power play.
"You have to win the special-teams battle to win games in this league," Stewart said. "We didn't score on the 5-on-3, and then we let them get two on theirs. That was huge."
The Wild made it 2-1 at 2:00 of the third period, with Eriksson Ek knocking Stewart's pass past Howard. Minnesota tied it 2-2 at 2:48 when Stewart was left alone at the edge of the crease to score off a Tyler Ennis pass.
"It's deflating to battle back into the game and then let it get away again," Boudreau said. "We took our foot off the gas, and hopefully we will learn from it."