Duchene and P.A. Parenteau scored in the shootout, and Colorado stopped a two-game skid with a 4-3 victory over the Winnipeg Jets.
Duchene also scored twice and added an assist in regulation. Ryan O'Reilly had a goal and an assist for the Avalanche (21-9), who trailed 2-0 after 5 minutes before Duchene scored late in the first period.
"We got behind the 8-ball in penalties," said Duchene, who hadn't scored in seven games after returning from a stomach injury. "They started really well. You've got to tip your hat sometimes. Getting that one kind of gave us some life and got the momentum going again, so it was a big goal."
Duchene's shootout goal beat Ondrej Pavelec after he lifted one leg and paused for a split second before firing the puck. Parenteau followed with a high shot over Pavelec's glove.
Colorado coach Patrick Roy was proud of his team for rebounding from the 2-0 deficit.
"That's the dangerous part of this because sometimes when you get behind you have the tendency to go individually and that's not what we did tonight," Roy said. "We (stuck) to the plan, we (stuck) together, we played as a team."
Duchene gave the Avalanche a 3-2 lead with his second of the night, scored with 1.6 seconds left in the second period. He backhanded a rebound into the open side of the net as Pavelec tried to slide back.
But Winnipeg used its fifth power play to tie it 3-all at 10:00 of the third period on Wheeler's second goal of the night.
Colorado wing Gabriel Landeskog put Winnipeg on its sixth power play when he was called for boarding after he checked defenseman Mark Stuart face first into the boards with 6 minutes left in the third. The Jets couldn't capitalize.
Winnipeg outshot Colorado 31-23 in regulation. The Jets had a 5-3 edge in overtime, with Pavelec making a big sliding stop on O'Reilly.
Just 24 seconds into the game, Wheeler spun around to the side of Varlamov and shot the puck. The rebound came out, hit the skate of defenseman Erik Johnson and went in for Wheeler's eighth goal.
The Avalanche killed a two-man power play, but with 22 seconds left on Nate Guenin's penalty, Jets rookie defenseman Jacob Trouba fired a one-timer from the point. Frolik stuck out his stick and redirected the puck past Varlamov at 5:25 for his eighth goal.
Duchene made it 2-1 with his team-leading 13th goal at 15:08 of the first when he went in alone on Pavelec and got a high shot past him.
Varlamov faced 38 shots, including five in overtime. Pavelec made 20 saves in regulation and three in overtime.
Jets coach Claude Noel lamented the loss of a point, but acknowledged Colorado's difference-makers.
"Duchene is a good player and (Nathan) MacKinnon's not a donkey, either. He's moving out there," Noel said.
Winnipeg outshot Colorado 14-4 in the first period, but the Avalanche turned the tables in the second, outplaying and outshooting the Jets 14-4.
The Avalanche went on the power play early in the second, but couldn't beat Pavelec. They haven't scored on their last 24 power plays.
Colorado tied it at 2 on O'Reilly's goal at 14:27.
The Jets also lost to Western Conference rival St. Louis 2-1 on Tuesday. They are 6-11-4 against their conference counterparts.
"Our division, our conference, isn't easy," Wheeler said. "There aren't any easy games.