The Ducks, who had scored three goals in their previous three games, completed a four-game road trip with a 3-1-0 record.
LaBarbera was recalled from Norfolk of the American Hockey League earlier Sunday because Frederik Andersen experienced tightness in his leg and didn't skate in the morning. LaBarbera, who played Friday and Saturday for Norfolk, was pressed into action when John Gibson sustained a lower-body injury in the warmup, prompting the Ducks to dress 45-year-old goalie consultant Dwayne Roloson as LaBarbera's backup.
"I haven't played a game in the NHL in over a year," LaBarbera said. "All of it is kind of goofy. I've been around a lot, never had to deal with something like this. Luckily came out on the right side."
The Ducks kept the Avalanche hemmed in their own zone for long stretches throughout the game, limiting them to 18 shots, seven after the first period.
"It's weird," LaBarbera said. "It's obviously nice, that means the team is playing well, doing some really nice things in the offensive zone. When you're already trying to get focused and not much going on, that makes it harder. The guys were great in front of me, blocking shots. I haven't been around this team, practicing and seeing them on TV and stuff. That was a pretty impressive effort."
The Avalanche went on a power play with 3:07 remaining in the third period and didn't get a shot on goal during the man advantage even after goalie Semyon Varlamov (30 saves) went to the bench for an extra skater.
"Considering the circumstances, I thought it was really good," Ducks coach Bruce Boudreau said of LaBarbera's play. "It wasn't the amount of shots or even the toughness of them. Just to be put into that position was a tough enough position.
"This is what makes it fun, doing things you're not supposed to do. Let's go out and win this one. Guys dig deep. They were the team that played last night, they were the tired team. We had the energy. I thought we had a lot of energy in the second and the third. We were getting on them and we weren't letting their skating game happen. When they're fresh they can skate like the wind."
The Ducks were especially effective in front of LaBarbera in the second period, when they outshot the Avalanche 12-2 and went ahead 3-2 on goals by Hampus Lindholm and Cam Fowler that came 1:44 apart.
LaBarbera didn't have to make a second-period save until defenseman Erik Johnson took a shot with 4:32 remaining. Rookie Dennis Everberg, who scored his first NHL goal early in the first period, had a shot from the neutral zone as the buzzer sounded ending the period.
"We don't really care who's in net, we have to take care of our side of things and we didn't do it in the second period," Avalanche center Matt Duchene said. "First period was great, third period was pretty good, we just lost the game in the second period. Two shots on a guy who obviously got called up at the last second isn't good enough."
Lindholm scored his first goal of the season at 6:04, a few minutes after Varlamov made a save against Andrew Cogliano on a shorthanded breakaway. Patrick Maroon was behind the net when he passed to Lindholm in the slot for a quick shot past Varlamov.
Fowler put the Ducks in front for the first time with his first goal of the season at 7:48. He skated from the left circle into the slot untouched for a backhander past Varlamov.
"I was joking with the guys that maybe there was a penalty on the play, the whistle had blown or something," Fowler said. "I almost couldn't believe it. Those guys were on the ice for quite a bit of time. Any time you get that, you get guys who are a little fatigued. I was lucky enough to make a good move. It's always good to get the first one out of the way."
Avalanche coach Patrick Roy said a major defensive breakdown led to Fowler's goal, which ended up as the winner.
"That third goal we were just lost," he said. "Jarome (Iginla) lost his position and it was an easy walk-in for Fowler. It was not a pretty period, that's for sure."
Everberg, playing in his eighth NHL game, scored 2:18 into the game when he skated down left wing into the Ducks' zone and took a shot from the bottom of the circle that skimmed between LaBarbera's pads.
"I've been around enough, you just kind of realize the circumstances and go, OK, whatever, this is really goofy but keep playing," LaBarbera said. "Don't worry about it, don't focus on the bad part, focus you're in a goofy spot and try to enjoy yourself."
The Ducks tied the game at 7:20 on Perry's NHL-leading 11th goal. Perry drove to the net and took a shot that hit Varlamov and bounced off Perry into the net as the players collided. The goal stood after a video review.
The Avalanche went ahead with 59.6 seconds left in the period when MacKinnon cut inside Ducks forward Devante Smith-Pelly in the right circle and beat LaBarbera with a shot to the far post.
MacKinnon has scored four goals in three games after going the first 10 games of the season without one.