Mats Zuccarello departed because of a first-period injury, but Marcus Johansson scored a go-ahead goal in the third period and Filip Gustavsson made 23 saves.
After a bleak October, Minnesota treated November as a dawning of a new year, going 11-1-2. They have a chance to surge in the standings in early December.
Buffalo scored a pair of unusual goals before tagging Filip Gustavsson three times in four shootout attempts, but going to overtime meant the Wild did record a point for the 11th game in a row.
Once considered a top prospect, an injury to the forearm nearly ended his NHL career before it started. Now Hunt is finding his place with the Wild and helping spark the turnaround.