It was the first time since Nov. 8 that Kaprizov failed to get a point, but it didn't hurt the Wild, who got a goal at even strength, one on the penalty kill and one on the power play to end a two-game skid.
"Our commitment level was real high here," coach Dean Evason said.
Filip Gustavsson made 35 saves for his first NHL shutout, and Mats Zuccarello had two assists for the Wild (14-11-2), who were coming off a 5-2 loss at the Edmonton Oilers on Friday and playing their third game in four nights.
"A relief," Gustavsson said. "It's been close. It was close my first ever game, lost it with five minutes left, and then I had a pretty close one this year with [the] San Jose [Sharks], where I screwed it up a little bit by myself there at the end. So, finally."