Spaling scored the game's first goal at 1:02 of the opening period.
From the right side, Matt Cullen's initial shot was denied by Phoenix goaltender Mike Smith. But skating through the slot, Spaling picked up the rebound and put it over Smith's right shoulder.
Craig Smith also assisted on the goal for Nashville, his ninth of the season.
Fisher doubled the Nashville lead at 8:22 of the first.
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