It was the first win of the season for the Wild, leaving New Jersey and Buffalo as the only teams in the NHL without a victory.
The winning goal came from Matt Cooke midway through the second period that snapped a 1-1 tie.
Harding needed to make only 14 saves to get the win while Ondrej Pavelec stopped 28 saves for the Jets, who have lost two in a row after opening the campaign with two wins.
Jonas Brodin scored on a slap shot 7:39 into the contest to give Minnesota the lead. Bryan Little tied it on the power play with 43 seconds remaining in the first period.