Shea Weber also scored as Nashville won for the third time in four games.
Rickard Rakell and Mike Santorelli had the goals for the Ducks, who have lost four of their last five. Frederik Andersen gave up three goals on 10 shots and was replaced in the second period by Anton Khudobin, who stopped all 11 shots he faced.
Weber scored the game's first goal at 9:33 of the opening period.
Rakell evened the game 1:14 later as he beat Rinne with a wraparound.
Nashville regained the lead for good when Neal sent a soft wrist shot that knuckled and squeezed between Andersen's pads. Salomaki scored his first of the season at 6:13 of the second to make it 3-1.
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