David Kampf scored, Nylander had an assist, and Ilya Samsonov made 24 saves for the Maple Leafs (36-15-8), who have won four of their past five games.
"I liked how we played just as disciplined a game," Toronto coach Sheldon Keefe said. "That's an elite defensive team. They play really hard, really adhere to their structure and tonight they were really dialed in in that area."
Brandon Duhaime scored, and Filip Gustavsson made 22 saves for the Wild (32-21-6), who had won four straight, including a 2-0 victory at the Columbus Blue Jackets on Thursday.
"We liked every part of our game here tonight except missing one point," Minnesota coach Dean Evason said. "That was a fantastic individual play (by Nylander). Gaudreau makes a great play himself getting stick on puck, but they do that a lot, they do a lot of stripping from behind. Their sticks are real good. Two inches up and it's a hook, but it wasn't, it was not on his hand, it was just on his stick. A very skilled play by a skilled player, and then a good play to beat a forward playing defense and then he makes a great move as well."