Calen Addison and Joel Eriksson Ek each had a goal and an assist for Minnesota (12-9-2), which has won three straight games for the first time this season. Filip Gustavsson made 29 saves.
"We're going to take two points, for sure," Wild coach Dean Evason said. "Two periods, we were not very good and they were good. They went to the net. They played hard. They scored their three goals in two periods … were tips, were screens at the net. They did exactly what we want to do. We played a perimeter game not willing to get to that area, and we almost got hurt by it. In the third period, we realized well, maybe we should play the right way. We were able to come back, and we're very fortunate that the game wasn't out of hand by the time we got to the third period."
Trevor Zegras and Troy Terry each had a goal and an assist for Anaheim (6-16-3), which has lost five straight games overall (0-3-2) and 12 straight against Minnesota (0-8-4). John Gibson made 43 saves.
The Ducks are 0-1-2 on their four-game trip, which concludes at the Winnipeg Jets on Sunday.
"It's one of those games like, man, you really want to get both points so that the team can feel rewarded for a good road game," Ducks coach Dallas Eakins said. "Overall, we did a great job. Goaltending was excellent straight across the board, and those are important to try to get both points, so there's a reward. But coming into a building like this and grabbing a point is certainly a step in the right direction. And we still have a chance to get .500 on the road here."