Mats Zuccarello scored in the second period and in the shootout, Joel Eriksson Ek had two assists, and Cam Talbot made 39 saves for Minnesota (17-6-1), which has a seven-game point streak (6-0-1).
"We did so many real good things," Wild coach Dean Evason said. "We had great looks. They did too. It was a real good hockey game. Real good hockey game by two really good teams. It was fun to be part of but whichever way it ended it was a good hockey game."
Jason Spezza had two goals and an assist, and Morgan Rielly had three assists for Toronto (17-6-2), which had won five straight overall and seven straight on the road to tie its record.
"It's a big point for us," Maple Leafs coach Sheldon Keefe said. "I love that our guys didn't go away at 3-0. They just dug in and wanted to make a game of it. We fought hard, we played well enough … All those things combined to give us a gutsy character point here on the road."
Auston Matthews extended his goal streak to five games, the sixth five-game goal streak of his NHL career. Only two players have had more with the Maple Leafs, Babe Dye (eight times) and Rick Vaive (seven).