The Islanders were 1-for-2 on the power play. The Wild were 0-for-3.
Quinn Hughes had a goal and an assist, and Joel Eriksson Ek and Matt Boldy scored for the Wild (9-3-3), who had won three straight. Jesper Wallstedt made 22 saves.
Minnesota lost its first home game of the season (4-0-1).
“I don’t think it was the cleanest game from us,” Minnesota coach John Hynes said. “We stuck with it, came from behind, and that’s what I talked to the team about. We didn’t have our A game tonight, but we gave ourselves a chance to win the game.”
Eriksson Ek made it 1-0 just 27 seconds into the first period with a wrist shot from the high slot.
“We didn’t let it get us flustered, or let them keep taking it to us,” Horvat said. “I thought we really made a push right after they scored there.”
Schaefer tied the game 1-1 at 16:36 with a wrist shot from the left circle on a rebound from Emil Heineman’s shot.
The Islanders took a 2-1 lead at 1:41 of the second period on Horvat’s backdoor tip-in from Simon Holmstrom on the power play.
Schaefer had the secondary assist to become the sixth teenage defenseman in NHL history with 15 career multipoint games. The others are Phil Housley (34), Ray Bourque (17), Larry Murphy (16), Rick Hampton (16) and Rasmus Dahlin (15).
"He's a heck of a player, for sure," Boldy said. "He showed it tonight. I don't think we did a good enough job of slowing him down, making his life a little bit harder. But credit to him, he plays the game like he's been playing for 10, 15 years. It's pretty fun to watch. Future is obviously pretty bright. They're pretty lucky to have him over there."
Hughes tied it 2-2 after he cut through the right circle and beat Sorokin five-hole with a sharp-angle, backhand shot at 17:21.