"Even at 3-0 I wasn't comfortable," Wild coach Bruce Boudreau said. "I mean, we weren't skating, they were beating us to every puck, they were outworking us. Even though we got three goals, it wasn't a 3-0 game at the time."
Cousins made it 3-1 at 11:30 after one-timing a cross-ice pass from Goligoski.
Kevin Connauton scored at 8:02 of the third period to cut it to 3-2, beating Dubnyk low glove side from the left circle.
"I think on the road, if you can score late in any period, it doesn't matter what it is, you sort of carry the momentum," Cousins said. "I thought, obviously, we carried play in the third period. It was nice to get one there."
Dubnyk made 36 saves for the Wild. Raanta made 25 saves for the Coyotes.
"[Arizona's] an NHL hockey team. It's not preseason," Dubnyk said. "They work hard. They got a bunch of young guys that are fighting for ice time and roles, and they worked hard. If you keep giving them the puck, bad things are going to happen."