Backstrom has 24 shutouts in his six-year NHL career, all of it spent with the Wild. His largest single-season total has been eight, set in 2008-09.
The game's lone goal came from Devin Setoguchi on a tip-in with just 2:31 remaining in regulation.
Minnesota, which has the early lead in the Northwest Division, has won three in a row and eight of its last 10. This was the opener of a six-game homestand.
Colorado has lost seven of eight overall and dropped five straight games on the road. The Avalanche won their first six road games this year.
Jean-Sebastien Giguere stopped 17 shots in taking the loss.