Dubnyk made 35 saves in his first win of the season and the Oilers beat the Ottawa Senators 3-1 on Saturday to break a long losing streak.
This victory came two days after Dubnyk stopped 37 shots on Thursday in a 3-2 loss to the New York Islanders.
"It's nice to get out there and be myself and just worry about playing goal," Dubnyk said. "It hasn't been an easy start, and it was nice the last two games just to relax and go play hockey and know that I can be ready for these guys."
Ryan Nugent-Hopkins scored two goals, including one into an empty net, to help Edmonton snap a five-game losing streak.
Jordan Eberle added a goal for the Oilers (2-6-1), who will finish a six-game road trip at Montreal on Tuesday.
The Senators continue to be one of the most penalized teams in the NHL. Ottawa took seven penalties, resulting in six power plays for the Oilers. None of them produced a goal.
"Penalties are not something we're going to forget about," Ottawa captain Jason Spezza said.
"It was a game where both teams were taking penalties, and it's not like other games where it was lopsided. We'll continue to talk about it until we start to take less penalties."
Senators forward Milan Michalek was called for goaltender interference when he ran into Dubnyk, and teammate Jared Cowen was given an interference penalty as the play continued down into Ottawa's end.
The Oilers generated only one good scoring opportunity on the ensuing power play as they tried to build on a 2-0 lead.
After the Senators killed off both penalties, they were quickly given a power play when Ladislav Smid was called for hooking. They were also unable to create anything offensively.
"It was good to see how calm the guys were after that," Nugent-Hopkins said. "We didn't get too much momentum off [the power play], and obviously not a goal which would have been huge, but we stuck with it and pulled out the two points."
Ottawa finally got on the board when Neil was credited with his first goal of the season on a shot that looked more like a missed popup than a hockey play.
Neil batted the puck out of midair, and Dubnyk appeared to try to catch the puck as it came down. Instead, it landed behind him and found its way into the net.
"We said in between periods that it wasn't going to be a pretty one that went in, and that's a prime example of a dirty goal," Neil said. "You go to the net and you get rewarded and we just didn't do enough of that. Their goalie was able to see way too much."
All the scoring before that came in the first half of the first period.
Edmonton scored on its first shot of the game after the Senators turned over the puck in the offensive zone. Eberle made a nifty move to get around Spezza and beat Lehner between the legs just 2:15 in.
A little more than eight minutes later the Oilers struck again. Lehner made a stop but was unable to control the rebound. The puck then went directly to Nugent-Hopkins, who scored from a sharp angle.
Oilers D Denis Grebeshkov made his season debut after missing eight games with a groin injury. ... Jesse Joensuu, Nick Schultz and Ryan Jones were scratched by the Oilers. Jean-Gabriel Pageau and Joe Corvo sat out for Ottawa. ... The Oilers had lost 39 man-games to injury going into Saturday, compared to only two for the Senators.