The last-place Wild now own two wins over the second-place Coyotes.
Minnesota is 1-5-3 since the All-Star break.
Eric Staal scored twice and Minnesota had two power-play goals.
Anaheim hadn't won a game since Dec. 17.
Devan Dubnyk was pulled after allowing three goals on 10 shots.
Matt Dumba scored twice and Mikael Granlund had three assists.
It was the 341st goal of Parise's career.
Mikael Granlund scored the go-ahead goal late in the third period.
The coach has a knack for leading teams on huge streaks, including last year's 12-gamer.
It's never good when you have to have microdisectomy surgery.
Parise will miss at least the first two games of the season.