Nolan fired a wrist shot past Cristobal Huet into the right corner of the net to complete a comeback win that began when the Wild rallied from four goals down in the third period to send the contest into overtime.
Niklas Backstrom played two periods in goal for Minnesota. He was pulled after giving up five goals on 12 shots. Josh Harding stopped all 13 shots he faced and allowed one goal on seven attempts in the shootout.
Marian Hossa, Patrick Sharp, Jonathan Toews, Troy Brouwer and Kris Versteeg scored for the Blackhawks, who had their five-game winning streak end. Huet made 16 saves in the loss.