Dubnyk made 37 saves -- including 23 in the third period -- and the Oilers scored all their goals on the power play to beat the Avalanche 4-1 on Monday night.
Ales Hemsky, Jordan Eberle, Shawn Horcoff and Nail Yakupov, into an empty net, scored on the man advantage for the Oilers (3-2-0). Taylor Hall and Sam Gagner each had two assists as Edmonton finally got a strong start to a game after falling behind in each of its first four outings.
"They had a really strong push at the end," Dubnyk said of the Avalanche. "You are able to get through things like that when you have earned a three-goal lead with how well we played in the first 40 minutes. There are going to be swings in momentum throughout the game. We wanted to get that first goal and get a lead, which we hadn't been able to do all year. It was good to see."
Oilers coach Ralph Krueger was glad to see his squad not have to dig itself out of a hole.
"The puck management through the first 40 minutes was an excellent reaction," he said. "It was an excellent first two periods all around, the kind of game we want to see on a regular basis.
"They pushed us in the third, and we had to buckle down and (Dubnyk) played excellent. But we showed in the first two periods that when (we) get teams down low and get moving like that, we are going to be a tough team to play against."
P.A. Parenteau scored for the Avalanche (2-3-0), who have lost two in a row to start a four-game road trip.
Avalanche coach Joe Sacco said his team once again got stung in odd-man situations after allowing three power-play goals in Saturday's 4-0 loss to San Jose.
"We put ourselves in short-handed situations again," he said. "We've allowed seven power-play goals now in two games. That's not good enough. The overall game was not good enough as well. We have to pick it up on our special teams, there is no question. And one goal in two games isn't going to get you many points."
Edmonton opened the scoring with five minutes to play in the first on the tail end of a power play. Hemsky swooped in and swatted a puck past Colorado goalie Semyon Varlamov during a scramble in front of the net.
The Oilers added another power-play goal with 2 minutes left in the period as Eberle picked the top corner on a shot from the top of the circle for his third of the season.
Edmonton had 14 shots in the first while Colorado managed only three on Dubnyk.
The Oilers took a three-goal lead midway through the second period on yet another man-advantage opportunity as Hall's shot hit Horcoff's skate in front and squeaked past Varlamov.
Colorado had its best chance to that point of the game a minute later as Jamie McGinn had Dubnyk beat but rang a shot off the post.
Persistent pressure by the Avalanche in the third finally paid off 8 minutes in as Parenteau fired a shot under Dubnyk's pads at the side of the net to make it 3-1.
Yakupov scored his third of the season on yet another power play with 30 seconds left and Varlamov on the Colorado bench for an extra attacker.
Varlamov finished with 23 saves.
It was the first of five meetings between the Northwest Division rivals. The teams split their six season meetings last season. ... The Avalanche were without captain Gabriel Landeskog, variously listed as out with leg and/or a head injury. Landeskog was leveled late in the first period by San Jose's Brad Stuart in Colorado's previous game but did return to finish the contest. ... The Avs remain without last season's leading scorer, Ryan O'Reilly, who is holding out due to a contract dispute. ... Edmonton made one lineup change, pulling newly acquired defenseman Mark Fistric for Corey Potter. ... The Oilers were without Ben Eager (concussion), Nikolai Khabibulin (hip) and Theo Peckham (hip), who are all day to day. Ryan Jones (eye) and Andy Sutton (knee) are out indefinitely. ... The Oilers went into the game having been short-handed 13 times in the first period in four games so far this season, the most in the NHL. They took two first-period penalties against Colorado and only three in the game.