Jamie Benn scored, and Jake Oettinger made 31 saves for Dallas (30-14-12), which has lost three in a row (0-1-2) and plays the Columbus Blue Jackets on Saturday.
"It was a great game," Oettinger said. "[Gustavsson] is a great goalie, made some huge saves. It felt like a playoff game. They're a great team over there. They're going to be a tough team to beat in a seven-game (playoff) series. It's tight out there. I had the chance to end the game in the shootout, [but] I didn't do it."
Zuccarello gave the Wild a 1-0 lead at 6:37 of the third period, deflecting a pass from Boldy on the power play.
"[Goals have] been hard to come by as of late, but yeah, it's a really good feeling," Zuccarello said.