Ryan Smyth added a goal and two assists to help Edmonton win its fourth straight.
"I saw some shots, quite a few shots, but I maintained my focus and kept playing my game," Dubnyk said. "The guys up front did an amazing job of blocking shots. It made it easier for me. Whenever the puck got past them to me, I was ready to make the save. It is noticable how hard our defensemen play."
Ryan O'Reilly scored for Colorado, which leads the league with six road wins but fell to 0-3 at home despite having a season-high 41 shots. Edmonton managed 19 shots.
"It's frustrating," Colorado right wing David Jones said. "We played pretty well most of the game. We put pucks on this goalie. Unfortunately, we had a couple of breakdowns at our end.
"It was a tough one. We still can take some positives on this game. It was one of those games where a couple of bounces went their way. Their goalie stood on his head and played a great game."
Both teams are off to good starts after finishing 29th (Colorado) and 30th (Edmonton) in the NHL last season. The game featured the first meeting between the top two picks in the NHL draft, Edmonton's No. 1 overall pick Ryan Nugent-Hopkins and Colorado's Gabriel Landeskog, the second overall selection.
In a taut defensive game, Barker broke through for the game's first score at 7:55 of the second period. With Edmonton on the power play, Barker took a pass from center Sam Gagner and skated across the crease before backhanding a shot past Colorado goaltender Semyon Varlamov.
Sutton made it 2-0 lead with 5:40 left in the period when his shot from the high slot found its way into the net over Varlamov's shoulder.
Colorado had several solid scoring chances but didn't convert until O'Reilly, with the Avalanche on their third power play of the game, put in a goal at 5:42 of the third to make it 2-1.
But just 27 seconds later, Edmonton regained its two-goal lead when Smyth scored his third of the season.
"Leave it to King Muck to do that," Oilers coach Tom Renney said of Smyth. "He was pretty much on his belly and swinging at it. It wasn't pretty but it was a pretty effective rush. Colorado comes at you. They've got good speed. Certainly, we had to push back somehow and that line did it and got us a very, very big goal."
- Edmonton has allowed only 14 goals in 10 games this season, an average of 1.4 goals per game.
- Barker's power-play score was the first allowed at home by the Avalanche penalty-killing unit.
- The game marked the first of six meetings this season between the Oilers and Avalanche, who split the series last year.
- The winning streak is Edmonton's longest since also winning four in a row from Nov. 29-Dec. 4, 2010.
- The Avalanche lost consecutives games for the first time this season.
- Smyth's three-point game was a season-high.