Ryan Nugent-Hopkins had a goal and two assists while Sam Gagne also scored for the Oilers, who have won their past two. Taylor Hall added the other goal and Viktor Fasth stopped 28 shots in the win.
Gabriel Bourque scored the only goal of the game for the Predators, who have dropped their last two contests. Pekka Rinne gave up five goals on 26 shots and was pulled halfway through the third, with Carter Hutton stopping all four shots he faced.
Edmonton scored the only goal of the first period when Gagner backhanded home a Martin Marincin shot in front of the net with 34.7 seconds showing on the clock.
Nugent-Hopkins scored on the power play at 8:18 of the second period for a 2-0 advantage.
Hall gave Edmonton a 3-0 lead with his shot from the left wing that hit just inside the right corner. It was initially not ruled a goal, but when play stopped around two minutes later the review showed that it was good as Hall nabbed his 23rd of the season at 14:48.
Nashville finally got on the board with 1:21 showing on the second period clock when Patric Hornqvist tried a wraparound from the left side that saw the puck come out front and Bourque snap it in.
Eberle had a pair of goals in the third period, both on the backhand from the left side, at 8:38 and 10:01 to blow the game open.