Carson McMillan's third-period goal was the 2, at Pepsi Center.
Justin Falk and Dany Heatley also scored for the Wild, who won back-to-back games for the first time since a seven-game win streak from November 28- December 10.
Niklas Backstrom stopped 24-of-26 shots as Minnesota put the brakes on an 0-9-2 road losing streak.
T.J. Galiardi and Chuck Kobasew lit the lamp for Colorado, while Jean- Sebastien Giguere made 31 saves as the Avalanche entered the All-Star break with a two-game losing streak.
"We just got away from our game tonight," Galiardi said. "It was pathetic with too many turnovers. It's frustrating because we don't play for six days. We'll have to regroup."
With the game tied at two in the third period, McMillan poke-checked the puck away from Colorado's Shane O'Brien near the Minnesota blue line and raced down the ice on a 2-on-0 breakaway. He then faked a shot in the slot before moving right and sliding the puck between the legs of Giguere at the 7:44 mark for the game-deciding goal.
"I don't get too many breakaways," said McMillan. "I was a little scared, but I found a hole and I was just glad to get it in and get the win."
Backstrom made 15 saves in the final period, including a blast from the right point by Stefan Elliot that was redirected in front in the final minute, to hang on for the win.
The Avalanche struck first just 4:37 into the opening period when Galiardi sent a backhander from the right circle that beat Backstrom to the short side.
But Falk tied the game at one with his first career NHL goal while on the power play with a wrister from the top of the left circle that went through a crowd in front at the 10:40 mark.
Heatley then sent the Wild into the first intermission with a 2-1 lead on his team-leading 15th goal of the season.
Kobasew netted the lone goal of the second period 4:46 in by cleaning up a Daniel Winnik shot from the left circle that dribbled past Backstrom and sat on the doorstep, waiting to be sent home.
Minnesota has won five of its last six games in Denver...Kyle Brodziak had two assists for Minnesota...Minnesota went 1-for-4 on the power play, while Colorado was 0-for-2 with the man advantage.