Pominville, obtained by Minnesota late last season after 10 seasons with the Sabres, worked a give-and-go play with Mikko Koivu as time was ticking down in the period.
After receiving the last in a series of quick passes, the right wing sent a shot off the shoulder of goalie Jhonas Enroth and into the net, breaking a 1-1 tie with his 22nd career winning goal.
Kyle Brodziak also scored as the Wild racked up a third straight win.
Josh Harding turned aside 22-of-23 shots for Minnesota.
Brian Flynn found the net and Enroth finished with 18 saves for Buffalo, which fell to 0-6-1 on the season.