Harding turned aside all 21 shots he faced in the second period and carried a shutout until late in the final period for Minnesota, which bounced back from a 4-0 loss at Columbus Friday.
Harding improved to 13-1-0 at home this season, posting a 1.25 goals against average and .945 save percentage over the 14 contests.
Parise's 13th goal of the season early in the second period broke a scoreless tie and his empty-netter with 6 second left in the third sealed the Wild's third victory in four games.
Mikko Koivu also scored for Minnesota, which won despite managing only 12 shots.
2014: The Year in Music [PHOTOS]