McGinn also scored the second goal on the powerplay a little later on, with assists going to Stephan Elliot and Peter Mueller, which ended up being his first goals as a member of the Avalanche and his 13th goal of the season since coming from the San Jose Sharks.
The Wild looked almost dominant in the second period, but they just couldn't find a way to get a puck past Semyon Varmalov, who stopped 30 shots for his fourth shutout of the season for the Avalanche.
Colorado outshot Minnesota 17-11 through 20 minutes.
The Wild won three of the first four meetings between them and Colorado. The two teams will play again Tuesday night in Colorado.