"We just wanted to get pucks back and get them to the net and it worked," Kunin said. "It was nice that our line was able to set a tone. We just wanted to keep it simple, get a lot of chances and get our bodies to the net. That's when good things happen."
Bratt pulled the Devils to within 3-2 with a backhand from the slot 3:56 into the third period, but Kunin made it 4-2 with a snap shot from the right face-off circle at 7:40.
Parise, who spent seven seasons with the Devils before signing a 13-year contract with the Wild on July 4, 2012, scored a power-play goal from the slot to give the Wild a 2-1 when he deflected in a shot from the right point by Ryan Suter 4:34 into the second. It was Parise's first goal in New Jersey since leaving.
Foligno scored off a backhand at the left post during a scramble after Schneider lost his stick to tie it 1-1 at 12:19 into the first period.
Seney gave the Devils a 1-0 lead off a wrist shot from the right circle 6:57 into the first.
"Their game plan is to keep teams to the outside and the way we score goals is to get to those areas and put pucks in the back of the net, and we weren't able to do that," New Jersey right wing Kyle Palmieri said.