Grubauer has won four straight starts, allowing a total of five goals.
"He's real confident, real sure of himself right now," Avalanche coach Jared Bednar said. "He's not giving up a lot of rebounds, he looks real strong down low. He's holding his ground down there and he's making the saves when we need them."
Kirill Kaprizov scored, and Cam Talbot made 29 saves for Minnesota (6-5-0).
"Both teams looked exhausted at the end," Wild coach Dean Evason said. "A lot of energy, really good hockey game, saw spurts back and forth. We thought we started real well, they pushed back, and we thought we finished extremely well. It was a battle. It was a really hard-fought hockey game that we felt could have gone either way."
The Avalanche took a 1-0 lead at 17:45 of the first period when O'Connor banked a shot off Talbot's pad.
"You're not going to see too many pretty goals from our line, we're just trying to muck it up a bit," O'Connor said of the fourth line with Sheldon Dries and Kiefer Sherwood. "We'll leave those pretty ones to [Mikko] Rantanen, Cale or whatnot. We want to play to our identity, get pucks to the net, get traffic, create those in-tight scrums, and just try and get greasy ones."
Nichushkin increased the lead to 2-0 at 7:09 of the second period when he scored on the rebound of a Joonas Donskoi shot from the left face-off circle.
"There's extra ice time that's getting distributed with the guys that we have out of the lineup, and I think some of those guys are eager to prove they deserve more ice time, and they're making the decisions tough," Bednar said. "Minutes are up for grabs on a nightly basis, and I thought the bottom six guys did a great job."