The result left San Jose as the only unbeaten team in the NHL.
Cullen also opened the scoring in regulation, putting the Wild in front 1:30 into the contest. The Blackhawks came back to lead after one period on goals by Andrew Shaw and Toews, but Cal Clutterbuck tied it just 59 seconds into the middle period and neither team could score for the rest of regulation.
Corey Crawford made 23 saves in the loss.
This was the opener of Chicago's six-game road trip. The Blackhawks will not play at home again until Feb. 12.
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