Andrew Cogliano, Ryan Jones, Jordan Eberle, and Dustin Penner scored for Edmonton, which ended a four game losing streak.
Dubnyk had to be sharp early with Nashville holding a 13-1 advantage in shots on goal through the first 10 minutes of the first period.
"We had a tough start, but that's my job to try and weather the storm," Dubnyk said. "I thought we controlled the game after the first period. With a 4-0 lead, it was tough not to watch the clock a little bit in the last five minutes."
The Predators have dropped five of their last six games.
Cogliano scored the game's first goal with just over 5 minutes left in the opening period. Eberle drove toward the Nashville net and sent a backhand shot on Predators goaltender Pekka Rinne from the left circle. Rinne stopped that shot, but the rebound landed in the low slot, where Cogliano was able to lift a backhand of his own over Rinne's glove.
"I thought we started to push back the last 5 minutes of the first and I think it gave them something to think about too, that if they don't get one here soon, that it may come back to haunt them," Edmonton coach Tom Renney said.
Nashville's captain admitted that first goal did affect his team.
"I think it was frustrating," Shea Weber said. "I think we kind of sagged on the bench. We did have a great first period, we had a lot of chances, and we just didn't capitalize. And credit to them, they did capitalize on their chances."
Jones, a former Predator, doubled the Edmonton lead early in the second. Colin Fraser had the puck on the right boards, where he fired a pass to Jones, who was skating through the slot. Jones had an easy tap-in for his 12th goal of the season.
"It was a great feeling since we've been struggling a little bit, and it is always great to get what turned out to the insurance goal and help the team out," Jones said. "It was a little extra special being back in this building."
The Oilers claimed Jones off waivers from Nashville on March 3, 2010.
Third period goals by Eberle and Penner ended Rinne's evening early, as he was replaced by backup Anders Lindback at 6:58 of the third. Rinne had 16 saves on 20 shots.
"They've got extremely skilled forwards, tons of speed, and you want to jump on them early and get them to doubt themselves a little bit," Nashville coach Barry Trotz said of the Oilers.
"They didn't have a lot of chances, and when they did have a chance, they buried it, not like us."
Material from wire services and team media was used in this report.
Backhand shot -
1 - 0 EDM
Snap shot -
2 - 0 EDM
3 - 0 EDM
Backhand shot -