Parise -- signed by Minnesota as a free agent along with defensemen Ryan Suter in July -- notched the game's only goal midway through the first period on assists from Pierre-Marc Bouchard and Dany Heatley.
Harding, meanwhile, turned aside all 24 shots he saw in racking up his seventh career whitewash for the Wild, who improved to 2-0 to start the lockout-shortened 2012-13 season.
Swedish goalie Christopher Nilstorp stopped 31-of-32 shots in his NHL debut for the Stars, who were coming off a season-opening victory over Phoenix Saturday.
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