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.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'