McMillan converted a mid-ice turnover into a breakaway and slipped a wrist shot past Jean-Sebastian Giguere to break a 2-2 tie and stake the Wild to their second consecutive win.
Justin Falk and Dany Heatley also scored for Minnesota.
The Wild had not won back-to-back games since a seven-game winning streak in early December.
Niklas Backstrom stopped 24-of-26 shots in the win.
Giguere turned in 31 saves for the Avalanche, who head into the All-Star break with two consecutive losses.
T.J. Galiardi gave Colorado a 1-0 lead in the first period and Chuck Kobasew scored in the second period.
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