Minnesota took a 2-0 lead into the locker room after 20 minutes on goals Carson McMillan and Charlie Coyle. New Wild defenceman Keith Ballard assisted on both.
Winnipeg (1-2-2) stormed back with second-period goals by Eric O'Dell, Patrice Cormier and Paul Postma. Minnesota defenceman Ryan Suter forged a 3-3 tie in the third period, scoring off a feed from Zach Parise.
Ondrej Pavelec made 33 saves for Winnipeg, while Niklas Backstrom had 28 saves for Minnesota, and stopped Blake Wheeler, Andrew Ladd and Bryan Little in the shootout.
The teams will play in the NHL's new Central Division this season.