Matt Duchene scored at 2:27 of the extra period after skating from the left corner while being checked by Jets left wing Dustin Byfuglien. The puck came loose when Byfuglien tugged at Duchene's elbow, but Jets defenseman Tobias Enstrom accidentally poked it back to Duchene, who backhanded a shot over goalie Al Montoya.
"I beat him with a move out of the corner and I was taking it to the net," Duchene said. "I saw (Ryan) O'Reilly for what I was hoping was going to be an open net. (Byfuglien) got my elbow, and the puck bounced off my stick. It bounced back to me and I took a whack at it. I didn't know it went in . I just heard the crowd cheering. Good bounce, nice to get that one."
The winning play spoiled the game for Byfuglien, who scored both Jets goals 1:48 apart in the second period.
"He got position, and the puck ended up back to him," Byfuglien said. ""A guy like that's never going to miss those."
Montoya finished with 31 saves.
"I don't remember it," he said of Duchene's goal. "I know the puck bounced in front of me, was poked in front of me."
Two days after losing center Paul Stastny to a back injury on his first shift Saturday, the Avalanche lost right wing PA Parenteau to a right-knee injury on his first shift. He is expected to miss the rest of the regular season.
"We showed a lot of character against a team that was playing very desperate," Avalanche coach Patrick Roy said. "It's a tough team to play against. They gave us a hard time. Just don't try to feel sorry for yourselves, this is what I said to the guys. We have to remain positive. All year we battled through adversity and tonight was another example. Our guys never stopped working. We played most of the game with three lines. Everyone chipped in, everyone played hard. It was a hard-fought game, no doubt about it."
Colorado (42-18-5), third in the Central Division, moved to within one point (90-89) of the second-place Chicago Blackhawks, who visit Pepsi Center on Wednesday.
"We're not out of the race for the division lead or No. 1 in the NHL," Duchene said. "We're right there. We just have to keep working hard here. I mean, that's a character win tonight. There's no other way to describe that. Guys just played their hearts out."
Winnipeg (30-28-8) earned a point to close within four points of the eighth-place Dallas Stars, who hold the second of two wild-card positions for the Stanley Cup Playoffs in the Western Conference.
"It was a good battle," said Jets coach Paul Maurice, whose team killed all six of Colorado's power plays and scored on its lone man advantage. "The penalty kill was outstanding, the power play -- what little we saw -- was 100 percent. I don't have a lot of complaints. I didn't think we gave up a whole lot. If you factor in the power play and penalty kill, both teams had some really good chances. We've got to find a way to draw as many (penalties) as we get."
"When guys go down, it's an opportunity for a lot of guys to step up in the lineup and try and contribute and make things happen," Mitchell said. "I knew I would be given more of an offensive role and try and play hard and play strong. I'm happy with the effort I put forth and I'm really proud of all the guys in here. We stuck with it even though we were shorthanded."
Mitchell set up Andre Benoit's goal with 11.2 seconds to play in the second period to tie the game 2-2. Mitchell won a draw from Olli Jokinen in the left circle and swept the puck back to Benoit at the point. Benoit moved in a few strides and fired a shot by Montoya, who was screened.
"Going into the third period being down one would have been tough," Mitchell said. "That was a huge goal for us and a big one for him to put home."
Byfuglien's two goals in the second period gave his team a 2-1 lead.
The Jets scored 23 seconds into their only power play of the game at 15:48 after Avalanche defenseman Cory Sarich was penalized for holding. Bryan Little took a shot that Avalanche goalie Semyon Varlamov stopped, but the puck squirted in front and Byfuglien was able to reach around defenseman Jan Hejda with his stick to sweep the puck inside the right post.
Byfuglien scored again at 17:36 after Varlamov made a save against Michael Frolik. The puck went behind the net, and Byfuglien poked it inside the near post by Varlamov's right skate.
Mitchell was credited with a goal, his first point in 12 games, to give the Avalanche a 1-0 lead at 4:38 of the second. He skated down the left wing and attempted to pass to MacKinnon driving to the net. MacKinnon and Jets defenseman Zach Bogosian got their sticks down, and the puck went in off Bogosian's blade.
"I don't score if Nate doesn't drive the net," Mitchell said. "Whether it went off a D-man or his skate, I made the pass, and Nate created the scoring chance by driving hard to the net."
Varlamov made a glove save against Jim Slater on a penalty shot at 13:01 of the first. Slater tried to pick the top corner of the net with his shot, but Varlamov knocked down the puck with his glove.
Varlamov made another big stop against Evander Kane with 1:30 to go in the period. Kane used his speed to skate down the left wing past Hejda. He cut across the slot for a shot that Varlamov stopped with his left pad.
"He made some clutch stops," Roy said of Varlamov, who finished with 33 saves for his 32nd win.
Jets center John Albert left the game at 6:11 of the second period with an undisclosed injury. He did not return.