Minnesota overcame a two-goal deficit in the second period and rallied from one down in the third but the Wild could not beat Ray Emery in the shootout.
Toews and Kane quickly ended the shootout with tallies in the first two rounds, sending the Blackhawks to their third straight victory. Minnesota has lost two in a row after winning seven straight.
The Blackhawks regained the lead on the 18th of the season from Toews 6:54 into the third and Mikko Koivu again deadlocked it with 5:04 to go in regulation.
Emery made 27 saves and Niklas Backstrom stopped 28 shots for the Wild before allowing the back-to-back shootout goals.