It was the 12 appearance in an NHL game for Kuemper, all of them with the Wild over the last two seasons.
Jordan Eberle scored the only goal for the Oilers 2:36 into the middle period, creating a 1-1 tie, but the Minnesota defense took over from there.
Defenseman Nate Prosser put the Wild in front for good with 3:15 to go in the second period. It was his first goal of the season and only the second of his career in 97 games spread over five years.
Justin Fontaine expanded the Minnesota lead to 3-1 with 1:03 to go in the second period and Jason Zucker scored on a deflection in the opening seconds of the third.
Ben Scrivens gave up the four goals on 33 shots.