Colton Sissons scored, and Pekka Rinne made 25 saves for Nashville (37-23-5), which has won three of its past four games and moved one point ahead of the Winnipeg Jets for first place in the Central Division.
Leon Draisaitl scored twice, and Mikko Koskinen made 36 saves for Edmonton (26-29-7), which has lost 12 of its past 15 games (3-8-4) and is seven points behind the Minnesota Wild for the second wild card into the Stanley Cup Playoffs from the Western Conference.
Draisaitl tied it 2-2 with a power-play goal at 9:12 of the third period, getting the rebound after Alex Chiasson’s initial shot was redirected by Ryan Nugent-Hopkins.
Draisaitl gave the Oilers a 1-0 lead at 2:08 of the first period on a shorthanded breakaway. He intercepted a pass by Predators forward Filip Forsberg in the neutral zone before beating Rinne five-hole with a backhand.
Sissons tied it 1-1 at 11:43 of the second period. Rocco Grimaldi received a pass from Subban on the rush and shot from the right circle, and Sissons got the rebound and scored into an open net.
Subban gave the Predators a 2-1 lead at 13:07 on a slap shot from the point. The goal was Subban’s 400th point in the NHL.
Forsberg and Brian Boyle scored in the shootout for the Predators.
The Oilers played without forward Connor McDavid, who was serving the second game of a two-game suspension for an illegal check to the head of New York Islanders defenseman Nick Leddy.