Minnesota tied the game with 11 minutes left in the third period.
After the teams traded goals to begin the shootout, three straight shots went by without a score. That led to Hemsky's effort, and he lost control of the puck as he headed for the net -- but goaltender Josh Harding fanned on it as the puck trickled through his pads and into the net.
Edmonton -- which won for only the second time in eight games -- got two goals and an assist from Shawn Horcoff.
Minnesota's James Sheppard scored his first NHL goal, as the Wild lost its second in a row. Minnesota lost in regulation for the first time this season Wednesday night.
The Oilers had dropped their previous six meetings with Minnesota.
Notable deaths of 2014 [PHOTOS]