"The way we started was great and we played a real solid game tonight," said Stastny. "Varlamov backed us up with some great saves early and kept us in it. The gates opened up there in the second period."
However, it wasn't all good news for Colorado as center Matt Duchene left the game in the third period with a right ankle injury and he will be evaluated on Wednesday.
Devin Setoguchi's penalty shot goal was the only score for the Wild, who have dropped their past five games.
Matt Hackett started the game in net, but was pulled in the second after allowing four goals on 21 shots. Josh Harding finished the game between the pipes and was tagged for three goals on 18 shots.
"It's very frustrating right now," said Minnesota center Matt Cullen. "I think that we have been very disappointed and everything is very difficult right now and that's an understatement. Everyone is trying, but we're just not doing the small things we need to do."
Jay McClement's goal 3:05 into the first was the only goal of the period to give the Avs a 1-0 advantage, but the team exploded for four in the second.
The first goal came at the 10:53 mark on the power play when Peter Mueller sent a hard pass from the left boards to the slot where McGinn redirected it home.
At the 14:38 mark, Hejda made it a 3-0 contest as his slap shot from the left point went through a screen. Less than a minute later, a 2-on-1 off a neural zone turnover saw Mark Olver score when he crashed the net on his shot.
With 3:26 left in the period, Colorado took a 5-0 lead after Ryan O'Reilly scored his 17th of the season.
Setoguchi scored on a penalty shot with a wrister to the left side of Varlamov 4:34 into the third, but Stastny and McLeod scored in the latter half of the frame to complete the rout.
Varlamov had a scoreless streak of 133 minutes and 23 seconds snapped on the penalty shot goal...Minnesota, which has been outscored 24-5 during its losing streak, plays at Phoenix on Thursday...Colorado plays in Nashville on Thursday...These teams split the six-game season series.