Mitchell scored at 3:35 of overtime, and the Avalanche beat the Minnesota Wild 2-1 on Monday for a rare win over their Central Division rivals.
''We hate these guys, to be honest,'' Tyson Barrie said. ''It's a rivalry for us and they've had our number over the last season and a half. This is a big win for us.''
The rivalry started when the Wild rallied from a 2-0 series deficit to beat Colorado in seven games during the 2014 Western Conference quarterfinals. Minnesota won four of five meetings last season and the first two this season. Four of those wins were shutouts.
''They've had our number here for a little while here now,'' Mitchell said.
Barrie had a goal and an assist and Semyon Varlamov made 19 saves for the Avalanche, who played in front of members of their 20th anniversary team. Sixteen of the 20 players selected were introduced before the game, as well as former team president and general manager Pierre Lacroix.
Ray Bourque, Peter Forsberg and Patrick Roy, the current coach, were given big ovations when their names were announced.
''You think back to the memories watching these guys, it's definitely a cool experience,'' said Duchene, one of four current players on the anniversary team. ''At the start of the year I was kind of secretly hoping to be on it. This is the organization I grew up pretty much worshipping. To be a part of this is really special.''
Kuemper finished with 18 saves and Zach Parise scored for Minnesota, which had won three in a row.
The Wild held a 44-20 advantage in shots on goal in Saturday's 3-0 win over Colorado, but the Avalanche cut down the chances Monday. Minnesota had just 13 shots through the first two periods and few clean ones on Varlamov.
''I'm sure they didn't want to play that same game they played the other night,'' Parise said. ''They wanted to try and slow us down with the neutral zone and counterattack. It was a lot tougher for us tonight.''
Colorado had gone five periods without a goal against the Wild when Barrie scored at 4:13 of the second. It was his fourth goal of the season and the first time the Avalanche had scored on Kuemper in four career games.
''It was a great pass by Carl (Soderberg) on that goal,'' Barrie said. ''I just had to go to the net and stop and it literally hit my stick and I had the whole net.''
Two of Kuemper's five career shutouts came against Colorado.
Devan Dubnyk, Minnesota's starting goalie, was injured during the second period of Saturday's win against Colorado. Kuemper replaced Dubnyk and made nine saves to get the victory.
The Wild tied it on Parise's eighth goal at 13:51 of the third period. It was Parise's first goal in 10 games.
''We have a couple of guys that could use a goal right now and Zach is one of them,'' coach Mike Yeo said. ''He's been pushing hard.''
NOTES: The Wild are 1-5 in overtime this season. ... Minnesota D Marco Scandella left in the third period after taking a puck to the face on a shot by Jarome Iginla. Scandella returned later in the game. ... Wild D Mike Reilly, called up on Wednesday, has yet to play. ... Colorado D Brad Stuart (back) has been out since Nov. 10. ... Minnesota G Niklas Backstrom served as Kuemper's backup. It is the first time this season he has been dressed.