Nichushkin has 10 points (seven goals and three assists) over his past six games.
Kurtis MacDermid scored the go-ahead goal early in the third period, and Ross Colton scored for the Avalanche (13-6-0) who have won two in a row and five of their past six. Alexandar Georgiev made 19 saves.
Colorado forward Tomas Tatar did not play. The reason was not disclosed prior to the game.
Kirill Kaprizov had a goal and an assist, and Joel Eriksson Ek scored for the Wild (5-9-4) who have gone 0-4-2 during their skid. Filip Gustavsson made 23 saves.
Colton gave the Avalanche a 1-0 lead at 17:43 of the first period off the rush, scoring from the left circle on an assist from Bowen Byrum.
Nichuskin made it 2-0 at 8:39 of the second period on the power play after tipping in a Nathan MacKinnon wrist shot from atop the left circle.
Kaprizov cut it to 2-1, scoring 34 seconds later at 9:13 when he deflected in a loose puck in the crease.
Eriksson Ek tied it 2-2 at 14:21 from the slot after redirecting a pass from Mats Zuccarello on the power play.
MacDermid put Colorado back ahead 3-2 at 4:56 of the third period with his first goal of the season, scoring off an assist from Andrew Cogliano after cutting through the slot.
