Jonas Brodin scored the game’s lone goal for the Wild (15-7-5), who have won 10 of their past 12 (10-0-2).
“I thought it was a really highly competitive game by both teams,” Minnesota coach John Hynes said. “I thought as the game went on, they had some pushes and I thought we did a good job defending and we got some good goaltending, a lot of blocked shots.
“It’s always a tough team to play against and I’m glad we found a way to win.”
Stuart Skinner made 23 saves for the Oilers (11-11-5), who had won two of three but were shut out for the first time this season.
“Obviously you’re disappointed any time you lose,” Edmonton coach Kris Knoblauch said. “You’re looking for the negatives, you look to critique the things we didn’t do. … But overall, I thought we played a game that more often than not would result in us coming out victorious and feeling good about ourselves.
“I’m disappointed that we lost but it was more of what we need.”
The Oilers were coming off a shutout of their own, 4-0, at the Seattle Kraken on Saturday.
“They defended well, obviously they’re playing well. Their goalie is playing well, they’re doing a lot of really good things,” Edmonton captain Connor McDavid said. “I thought there were some good signs. We played real solid in Seattle. I thought we played another pretty decent one here today. That’s a good sign.
“I thought we generated looks. We only gave up one. Usually when you give up one, you’re going to win a lot of games. We didn’t.”
Brodin put the Wild ahead 1-0 at 13:11 of the first period with a one-timer near the blue line off the face-off win by Nico Sturm, beating Skinner glove side.
“I thought it was a good game; I thought ‘Wally’ was really good in net. I thought we defended really hard,” Brodin said. “I think maybe the next game, we can be a little bit better offensive probably.
“But other than that, I thought it was a great game and ‘Wally’ was so good and made a lot of really good saves.”