The Wild (4-2-1) were thoroughly outplayed and were completely out of gas as the Blackhawks held a 25-10 edge in shots on goal over the final 45 minutes.
Niklas Backstrom took over from there.
The Finnish goaltender started the game on the bench, but was called to action when Josh Harding allowed two goals on four shots (not including a wrist that rang off the post) in the first six minutes and 45 seconds of the game.
"Sometimes you need to do that to spark the team or just change it up," Matt Cullen said. "I think its important that everybody understands that we have so much confidence in (Harding). It is just one of the those things they get a couple quick ones and change is needed."
Cullen banged away at a rebound to score his first goal of the season. The veteran forward has had numerous opportunities this season, but finally broke through Wednesday.
"Every player would be lying if they said they didn't," Cullen said about having a big lifted off his shoulders by scoring. "You always want to contribute on the scoresheet."
Cullen later anchored the Wild's shootout lineup and scored his eighth career shootout deciding goal.
For the first time this season, the Wild's top line was left off the scoresheet and second and third lines did all the contributing.
The Blackhawks (6-0-1) entered the game tied with San Jose Sharks for the best record in the NHL.
No. 3 – Andrew Shaw. The Blackhawks forward scored the Blackhawks first goal.
No. 2 – Matt Cullen. The Wild forward scored a goal.
No. 1 – Niklas Backstrom. The Wild goaltender stopped all 28 shots he faced and two of three shooters.
Chicago 2 0 0 0 – 2
Minnesota 1 1 0 0 – 3
First Period – 1, Minnesota, Cullen 1 (Setoguchi, Granlund), 1:30. 2, Chicago, Shaw 1 (Bickell, Kane), 5:14. 3, Chicago, Toews 4 (Hossa), 6:45. Penalties – Konopka, Min (interference), 13:57; Stalberg, Chi (interference), 15:30; Frolik, Chi (boarding), 16:08.
Second Period – 4, Minnesota, Clutterbuck 1 (Gilbert), :59. Penalties – Kruger, Chi (holding), 14:22.
Third Period – None. Penalties – Stoner, Min (interference), 5:51; Sharp, Chi (hooking), 17:95.
Overtime – None. Penalties – None.
Shootout – Chicago Toews (goal), Kane (saved), Sharp (missed). Minnesota Parise (goal), Koivu (missed), Cullen (goal).
Shots on goal – Chicago 7-8-11-6 32. Minnesota 15-4-2-4 25.
Goalies – Chicago, Crawford (23-25). Minnesota, Harding (2-4), Backstrom (28-28). A – 18,550. Referees – Tom Kowal, Brian Pochmara. Linesmen – Don Henderson, John Grandt.