It was quite a day for the 25-year-old Varlamov, who also finalized a five-year contract extension with Colorado that runs through the 2018-19 season.
The Avalanche won the season series with the Wild 4-0-1 and moved nine points ahead of them in the Central Division. Colorado has a firm grasp on third place and the final automatic playoff seed in the division.
The Avalanche used a big second period to help cool off the Wild.
Mitchell broke a 1-1 tie with his sixth goal of the season at 1:43. Stastny scored his 16th of the season on a rebound midway through the period, and Talbot used the stick of Wild center Kyle Brodziak to make it 4-1 at 15:26. Brodziak had gathered a rebound in front of goalie Darcy Kuemper when Talbot came in from behind and hit the center's stick to put the puck in the net.
A minute later, Niklas Backstrom replaced Kuemper, who had 19 saves.
Backstrom had nine stops the rest of the way, giving the Wild a chance to get back into it. Parise's goal at 7:47 made it 4-2. He then assisted on Granlund's goal at 12:51 that made it a one-score game.
MacKinnon appeared to seal the win with his 19th of the season at 17:35 but Pominville scored 11 seconds later.
Backstrom went off for an extra skater with 1:07 left but the Wild couldn't get the equalizer.
Colorado took a 1-0 lead on O'Reilly's 20th of the season at 4:41 of the first and Parise tied in on the power play 1:35 later.
The Avalanche had three power-play chances to break the tie in the first but couldn't capitalize. Brodziak nearly scored a short-handed goal but Varlamov made a save on the odd-man rush.
NOTES: Avalanche RW P.A. Parenteau was a healthy scratch for the second straight game. Parenteau played in three games after missing 10 with a sprained left knee. ... Wild D Jared Spurgeon skated with the team Thursday. He has been on injured reserve since Jan. 4 with a foot injury.