Dubnyk held Nashville at bay down the stretch as the Oilers got third-period goals from Lennart Petrell and Jordan Eberle to break open a 1-1 contest.
Petrell's go-ahead goal midway through the final frame came as Edmonton was shorthanded and provided the momentum the Oilers needed to log their third victory in four games.
Shea Weber and Roman Josi scored for Nashville, which dropped all three games of a Western Canada road swing.
Pekka Rinne made 18 stops for the Predators.
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