The win pushed the Oilers into first place in the Northwest Division one point ahead of Colorado and extended their season-high unbeaten streak to six (4-0-2). Nashville dropped its fourth straight.
Salo, 29, has been a workhorse, appearing in 49 of the Oilers's 58 games.
"Tommy has been absolutely fantastic for us," Oilers forward Bill Guerin said. "He really is having an All-Star year."
Devereaux put a short-handed tally past Nashville goalie Tomas Vokoun at 9:37 on a floating shot from the high slot.
Murray made it 2-0 at 16:23 with a high wrist shot from the left side after Josef Beranek set the play up with a pass from the right circle.
"For sure it gets tougher every night," Predators defenseman Drake Berehowsky said. "But we're still going to stay positive and we're going to keep working to make the playoffs."
Nashville's Vitali Yachmenev cut the lead to 2-1 at 6:54 o the second, firing a high wrister over Salo.
"It is frustrating but I think we had a lot of opportunities," Berehowsky said. "We might have missed quite a few shots, but we didn't play a full 60 minutes tonight and that's why we're most disappointed."
Nashville forward Sergei Krivokrasov returned to the lineup for the 350th game of his career after being a healthy scratch Saturday. Krivokrasov led Nashville with 25 goals last season, but has scored just nine in this campaign and has been a defensive liability.
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