Duchene also scored twice and added an assist in regulation and Ryan O'Reilly scored a goal and added an assist for the Avs (21-9-0).
Duchene scored his second goal of the night to give the Avalanche a 3-2 lead with 1.6 seconds left in the second period when he backhanded a rebound into the open side of the net as goalie Ondrej Pavelec tried to slide back.
But Winnipeg used its fifth power play to tie the game 3-3 at 10:00 of the third period after Mark Scheifele sent a shot from the point that Wheeler put in past a screened Semyon Varlamov with two seconds left in a tripping penalty to Cory Sarich.
Avs winger Gabriel Landeskog put Winnipeg on its sixth power play of the night when he was called for boarding after checking defenceman Mark Stuart face first into the boards with six minutes left in the third, but the Jets couldn't capitalize.
Winnipeg outshot Colorado 31-23 in regulation. The Jets had the 5-3 edge in shots in overtime, with Pavelec making a big sliding stop on O'Reilly.
The Jets went on the power play three times in the first seven minutes of the game, including a 36-second two-man advantage.
But it was an even-strength goal that got the crowd cheering 24 seconds into the first period when Wheeler spun around to the side of Varlamov and shot the puck. The rebound came out, hit the skate of Avs defenceman Erik Johnson and went in for Wheeler's eighth goal of the season.
The Jets got on the power play two minutes later when Johnson went to the box for holding. Colorado then handed Winnipeg a 36-second two-man advantage after defenceman Nate Guenin was called for delay of game when his shot went over the glass.
The Avs got through the two-man advantage, but with 22 seconds left in Guenin's penalty, Jets rookie defenceman Jacob Trouba blasted a one-timer from the point and Frolik stuck out his stick and redirected the puck past Varlamov at 5:25 for his eighth of the season.
Duchene made the score 2-1 with his team-leading 13th goal of the season at 15:08 of the first when he went in alone on Pavelec and got a high shot past the netminder.
Winnipeg outshot Colorado 14-4 in the first period, but the Avs 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 in their last 23 power plays and the number went to 24 midway through the period.
The Jets couldn't do much on their fourth power play and then the Avs kept the pressure on for O'Reilly's goal to tie it 2-2 at 14:27.
Duchene changed directions behind the net and passed the puck to O'Reilly, who got it behind Pavelec.
Notes: With the win, the Avalanche equalled their most wins through 30 games in franchise history (21 in 2000-01 and 1994-95) … Winnipeg has played 20 games decided by a single goal this season and is 7-8-5 in those games … The Avs are 18-0-0 when ahead after two periods and 2-0 in shootouts this season.