Gabriel Landeskog and Nathan MacKinnon had a goal apiece to help the Avalanche sweep the home-and-home series with the Wild.
John Mitchell added two assists for Colorado, which won a rare penalty-free game.
Mikko Koivu and Matt Cooke scored goals and Josh Harding stopped 23 shots for the Wild.
Minnesota has dominated the Avalanche in Colorado since the 2007-08 season. The Wild came into Saturday with a 12-2-2 record since midway through that season, and they had won six of their past seven at Pepsi Center.
The Avalanche looked as if they would win comfortably when Cooke spoiled the shutout bid with 3:27 left to make it 2-1.
Harding came off for an extra skater in the final minute, and Koivu beat Varlamov on a slap shot with six seconds left to send the game into overtime.
Neither team could score in the extra period, sending the Avalanche to their first shootout of the season.
Harding and Varlamov made saves on the first two shooters before O'Reilly broke through. Jason Pominville couldn't match the goal and Minnesota lost for the second straight night.
Coming off a tough loss to Colorado in St. Paul on Friday night, Minnesota was looking to get even but Saturday's game started like Friday's ended.
Landeskog, who sealed Friday's 3-1 win with an empty-net goal, gave the Avalanche the early lead when his backhand from the side of the net deflected off Harding and into the goal 2:22 into the game. It was his ninth goal of the season.
The Wild nearly tied it later in the first when Cooke's backhand slipped under Varlamov and lay on the goal line for a moment and the goalie covered it up. It was reviewed and determined the puck never completely crossed the line.
Minnesota had another great chance in the second period when Torrey Mitchell got ahead of the defense, took a pass from Cooke and had a breakaway on Varlamov. The goalie stopped the backhander to preserve the one-goal lead.
Colorado added to the lead later in the second when Marco Scandella turned it over in his own end. Mitchell got the puck to a wide-open MacKinnon, and the rookie beat Harding with a wrister at 12:56 of the period.
It was his fifth goal of the season.
Mitchell reached 100 career points with his two assists. ... Wild LW Zach Parise played in his second straight game after missing one with a foot contusion. ... Avalanche C Paul Stastny returned after missing two games due to back spasms.