Justin Fontaine and Jason Pominville scored for the Wild, who ended a three-game losing streak.
Fontaine scored the decisive goal at 18:53 and Pominville knocked in an empty-net score in the game's closing seconds. Zach Parise assisted on both goals.
Harding faced just three shots in the first period, six in the second and seven in the third.
Nashville's Pekka Renna was much busier. He stopped 27-of-28 shots, but it was not enough to extend the Preds' two-game winning streak.