Nico Sturm broke a tie off a misplayed puck by Ducks goalie Ryan Miller to make it 3-2 at 7:01 of the second period.
"Yeah, it was a fluky one, but they don't ask how, right?" Wild defenseman Ryan Suter said of Sturm's goal, which came after Miller failed to cover the puck on a dump-in.
Jared Spurgeon scored twice, and Cam Talbot made 28 saves for Minnesota (20-10-1), which has won two in a row and seven of nine.
"We didn't play our best, but the good thing is we know that," Spurgeon said. "We're not sitting here saying we played a great game. We have a big test tomorrow (against the St. Louis Blues) and we have to get ready for that one."
Derek Grant and Max Comtois scored for Anaheim (9-19-6), which lost here 2-1 on Monday. Miller made 23 saves.
"I'm not going to lie, it's hard. It's extremely tough [in these losses]," Ducks coach Dallas Eakins said. "We've got all of our guys tonight, basically to a man, work their tails off. They were very in sync in a lot of the game. I have very little issues with our play. I thought we played hard, I thought we played smart. We got a bad bounce that ends up in our net."