The play went under review for several minutes, before the referee announced it no good, drawing boos from the crowd.
Jean-Sebastien Giguere rested after hurting his groin the night before, giving the start to Varlamov. Giguere went out late in the third against Phoenix and Varlamov helped the Avalanche to a shootout win.
Varlamov, who turned 25 on Saturday, was kept quite busy by the Wild, stopping 30 shots.
This might have been the last NHL game for Colorado's Milan Hejduk, who grabbed the final puck just in case he's not back for a 15th season.
"I haven't made up my mind. I will take some time off to consider it and then make my decision," he said.
It's been a tough season for Hejduk, the last remaining link to the 2001 Stanley Cup squad. He had a career-low 11 points and missed time with shoulder and torso injuries.
The 37-year-old Hejduk is second in franchise history in games (1,020), fourth in goals (375) and fifth in assists (430). He's also just the third Czech-born player to reach 800 points, joining Jaromir Jagr and Patrik Elias.
NOTES: The Wild recalled Fs Stephane Veilleux and Jason Zucker from Houston of the American Hockey League before the game. Veilleux was a scratch. The team also reassigned forwards Jake Dowell and Carson McMillan to Houston. ... Colorado Fs Matt Duchene and P.A. Parenteau each finished with 43 points. The only previous time in the franchise's history it had teammates share the squad's scoring title was 2008-09 when Hejduk and Ryan Smyth each had 59 points.