Alexander Radulov, Shea Weber, Ryan Suter and Vernon Fiddler scored the Nashville goals.
The Predators (48-21-7) moved two points ahead of the Detroit Red Wings for top spot in the Western Conference and the Central Division after the Wings had moved into a temporary tie for first with a point from a shootout loss earlier in the day.
The Oilers (31-38-7) have only one win in their last 14 games and spend the last six games of the regular season on the road.
Nashville got off to a 1-0 lead just 4:28 into the first period as Peter Forsberg picked up a rebound at the side of the net, and he found Radulov open in front for an easy tap in past Oilers starter Jussi Markkanen.
The Predators opened the game up six minutes into the second with two goals in just a 25 second span. Weber blasted a shot from the right point on the power play that beat Markkanen through his pads to put Nashville ahead by two. Nashville made it 3-0 less than a minute later as Suter's point shot took an odd bounce past Markkanen before defenceman Bryan Young could prevent the puck from crossing the line.
Edmonton outshot Nashville 20-17 through the first 40 minutes but couldn't get one past Vokoun.
The Preds padded their lead with another early goal in the third as Marek Zidlicky sprung Edmonton native Fiddler and his slap-shot cleanly beat Markkanen to make it a four-goal game.
The two teams play a rematch in Nashville on Tuesday as the Predators start a five-game homestand.
NOTES: With another crowd of 16,839 the Oilers sold out all 41 of their games at Rexall Place in Edmonton this season. They have now filled the building for 73 consecutive games stretching back to Nov. 29, 2005a Oilers forward Ales Hemsky was forced to sit out the game, still suffering from a shoulder injury. He dressed against the Avalanche on Friday and made an impact, scoring a goal to help Edmonton break their 12 game winless streak with a 4-3 shootout win. Also scoring for the Oilers in regulation were a couple of guys who hadn't in a while. Petr Sykora broke a 15-game scoreless drought and Joffrey Lupul found the net for the first time in 18 outingsa As well documented as the Oilers injury woes have been, currently with seven players out, the Preds are also feeling the pinch with four players (Scott Hartnell, Steve Sullivan, Martin Erat and Scott Nichol) injured and Jordin Tootoo serving a suspensiona Nashville is now just four goals shy of matching the franchise record for goals (259), set last season.