Ales Hemsky recorded his first career hat 3, at Bridgestone Arena.
Darcy Hordichuk, Ryan Jones and Sam Gagner also tallied goals for Edmonton, which won for the third time in four games. Devan Dubnyk made 41 saves in the victory.
Pekka Rinne started the game for Nashville but was pulled after allowing three goals on seven shots. Anders Lindback relieved Rinne and stopped 10-of-12 shots.
Edmonton struck first at the 12:50 mark of the first period when Hordichuk's attempted centering pass from behind the goal line to the right of the net deflected off the skate of Nashville defenseman Kevin Klein and past Rinne.
The Oilers added to their lead at the 16:22 mark of the first after Hemsky and Gagner raced down the ice on a 2-on-1 rush. Hemsky cruised down the left side of the zone before cutting to the right and firing a wrister into the top-left corner of the net as Rinne got bumped into by Gagner, who was forced into the goaltender by Predators forward Martin Erat.
Nashville was able to close the gap to 2-1 in the closing seconds of the opening frame when Legwand cleaned up a loose puck in front of the net with 6.8 seconds remaining after an offensive flurry by the Predators.
Edmonton, though, regained its two goal advantage just 28 seconds into the second period when Hemsky lifted his own rebound over the left shoulder of Rinne, ending the goaltender's night.
Jones' power-play tally at the 5:51 mark of the middle stanza gave the Oilers a 4-1 edge before the Predators answered with a power-play goal of their own.
After failing to convert on a minute and a half two-man advantage, Nashville capitalized on the brief 5-on-4 power play with Hornqvist's second goal when he finished off a tic-tac-toe play in the slot.
But Hemsky stole the puck off of Predators forward Matt Halischuk in the neutral zone and finished off a breakaway opportunity with a wrister past Lindback's glove side with 5:57 left in the second for his third goal of the contest.
Legwand brought Nashville within two again just 4:18 into the third when his backhander from behind the net bounced into the net off Dubnyk's back, but the Predators would not score again and Gagner's empty-netter sealed the win for the Oilers.
Hornqvist had a goal overturned in the second period because of goaltender interference...The Oilers improved to 22-3-2 this season when leading after two periods...Nashville went 1-for-4 on the power play, while Edmonton was 1- for-1 with the man advantage.