The Wild won for the seventh time in nine games.
Martin Havlat put Minnesota in front for good by finishing off a bizarre stretch that saw the teams combine to score three goals in 51 seconds late in the opening period.
Minnesota's Antti Miettinen and Colorado's David Jones had scored 11 seconds apart before Havlat's wrist shot gave the Wild a 2-1 lead with 4:09 to go in the period.
John Madden scored the only goal of the second period to give Minnesota a 3-1 lead and that became the game-winner when David Jones tallied for Colorado 23 seconds into the third.
Backstrom then shut the door and handed the Avalanche their fifth straight loss.
After giving up three goals on 17 shots, Colorado's Craig Anderson was removed in favor of Peter Budaj.
Minnesota has won nine of its last 12 meetings with Colorado.