He fired a shot on Ray Emery that got between the Chicago goalie's pads, handing Minnesota its first three-game winning streak since early December.
Dany Heatley, Kyle Brodziak and Clayton Stoner also scored for Minnesota, which has been eliminated from playoff contention.
Josh Harding earned the win with 31 saves.
Kane's second goal of the game with 2:45 remaining in regulation forced overtime for the Blackhawks, who clinched a playoff spot Saturday with a 5-4 victory over Nashville.
Patrick Sharp and Viktor Stallberg got Chicago's other goals.
Emery finished with 26 saves.