Cam Talbot made 27 saves, and Kirill Kaprizov had two assists for Minnesota (45-21-6), which has won two straight and is 11-1-2 in its past 14 games.
The Wild remained tied for second in the Central Division with the St. Louis Blues, who defeated the Boston Bruins 4-2 on Tuesday.
"We were happy with the way we played," Minnesota coach Dean Evason said. "… We talked before the game that we shouldn't have to talk about our start. We should just be playing. We should just play like we play. That's what we did and that's how we play. That's when we have success. We're in on pucks, we're dislodging, we're having good sticks and we're getting opportunities because of it, and not only in the offensive zone, but in the defensive zone, too. We exited real well. They had a couple of sustained shifts, but for the most part we did a lot of real good things."
Leon Draisaitl scored his NHL career-high 51st goal for the Oilers (42-26-6), who have lost two in a row (0-1-1). Mikko Koskinen made 18 saves.
"Today wasn't our finest hour," Edmonton coach Jay Woodcroft said. "We didn't come away with any points in a tough building. We can play better."