Ryan Hartman, Kevin Fiala and Marcus Foligno scored for the Wild (7-6-0), who have split two games since returning from a two-week shutdown caused by NHL COVID-19 protocols.
Minnesota had six games postponed and as many as 13 players in the protocol.
"We've got to pick up some wins and climb the standings a little bit, so this one can jump-start us," Foligno said. "It wasn't pretty, and it wasn't our best, obviously, but we know we're going to get better and better."
Sam Steel scored, and John Gibson made 24 saves for the Ducks (6-8-3), who scored two goals or fewer for the 13th time.
"After a number of games where we really thought we were going in the right direction with creating chances, having lots of action, this was a big stop sign," Anaheim coach Dallas Eakins said. "It's certainly going to be a big reset for us."
Anaheim was active in the Minnesota zone during the first period, but its first 13 shots were either blocked or off target. It didn't have a shot on goal until 16:25 of the first period. By then, the Wild had a 2-0 lead on goals by Hartman and Fiala.
"We start that game, we've got great pressure," Eakins said. "We're just looking for some kind of reward there, and then when you don't get it, it's quite deflating."