Barrie got the Avs started offensively with a power-play marker 8:16 into the second frame. He was playing in his first game since Nov. 24, as he missed the team's last four outings with a lower-body injury.
Soderberg netted Colorado's next goal and Nieto completed the comeback with the fourth short-handed tally of his career.
Colorado recorded 18 shots in the first frame and finished the outing with 45 overall, a season high and the team's most since Dec. 31, 2017 against the New York Islanders.
"Erase seven and a half minutes out of that game and I liked what I saw on both sides of the puck," Bednar said of his team's performance. "The reason we were getting those chances and those shots even in the first period and scoring chances and why we came back in the second is because we were playing the right way. We didn't manage the puck very well [during those seven minutes], we turned the puck over a handful of times.
"I have four of our goals against on turnovers, one off a faceoff and one on the power play. So, we have to do a better job at taking care of the puck on some of those breakouts and winning some of those wall battles that they beat us to the net on."
The outcome of the game is Colorado's first regulation loss since Nov. 9 at the Winnipeg Jets, 25 days ago. The Avs had at least a point in each of its previous 11 games, going 9-0-2 during the stretch, and had won six straight on the road.
"We have to have a short memory, that's what we have been preaching when we have been 9-0-2," said Bednar. "I don't care what they did yesterday or the day before and the week before that, I am worried about the next game and that's the way our whole team thinks and that's the way we approach it. It's why we have been able to sustain the point streak, and now we have lost and the message doesn't change. Its consistent.
"We want to make sure that we respond and get back at it the next game. There will be a lot of good stuff out of that game that we really like, but there are some turnovers in the seven-minute stretch at the start of the game and two or three minutes in the third there where we have to better than what we were if we want to win. We gave up some home-run plays there, and we have to be better than that."