Antti Miettinen, Martin Havlat and John Madden scored for the Wild, who overcame a two-goal game by David Jones. The Avalanche, still waiting on Peter Forsberg's visa clearance, played without captain Adam Foote and lost another defenseman, Kyle Cumiskey, to a head injury in the first period.
The Avalanche fell to 3-8 in their last 11 games, and Craig Anderson lost his sixth straight start, giving up 21 goals over those games. He was pulled in the second period for Peter Budaj.
Backstrom improved to 16-4-2 in 22 starts against the Avalanche. He has given up two goals or less in five of six starts, with wins in four to help the Wild climb back in the Western Conference playoff race.
The first period featured three goals in a 51-second span. With Andrew Brunette screening Anderson and then deftly lifting defenseman Ryan Wilson's stick, Miettinen's power-play slap shot sped past Anderson to make him the eighth Wild player with at least 10 goals this season.
Just as the public address announcer was giving the recap, Jones snatched a loose puck off a faceoff and sent a shot between Backstrom's legs to tie it and prompt a groan from the crowd.
Havlat, however, responded with his team-high 15th goal. The All-Star produced one of his finest goals in two years with the Wild, muscling the puck away from Paul Stastny behind the net and pivoting to push a backhander past Anderson.
Jones could have had a hat trick, but his goal in the second period was immediately waved off, a ruling confirmed by the replay officials.
Madden, with Brad Staubitz screening Anderson, followed a few minutes later by reaching forward and zipping a snap shot into the back of the net as he did the splits. Budaj was summoned from the bench after that.
The Wild improved to 12-4-1 in division games, getting an important bounce back from a 1-0 loss at Phoenix on Saturday.
The Avalanche caught a break 23 seconds into the third period when Wild All-Star defenseman Brent Burns gave the puck away along the back boards. Jones snagged it and flipped a pass from behind the net that appeared to deflect off Minnesota's Nick Schultz in flukey fashion before pinballing in the net to cut the lead to 3-2.
Burns drove hard to the net midway through the final frame, aggression that the Avalanche didn't like, prompting a fight that sent three players from each team to the penalty box. Havlat and Wilson were involved in the most intense tussle.
Notes: Brunette was given a watch, a commemorative silver stick and a $15,000 check for his hometown youth hockey association in Ontario in honor of reaching 1,000 career games last week. Brunette's brother and his golden retriever led the crowd in the traditional "Let's Play Hockey!" chant before the puck drop. ... Wild C Matt Cullen, who returned from a one-game absence due to an upper body injury, notched his second multi-assist game of the season and the first since Oct. 16. ... The first intermission was stretched out by a few more minutes due to a Zamboni malfunction.