Atkinson scored with five minutes left in regulation for a two-goal lead.
James Neal scored for Nashville during a two-man advantage with 1:33 remaining, but the Predators couldn't get the equalizer against Bobrovsky, who denied Mike Ribeiro's penalty shot earlier.
Eric Nystrom had the other goal for the Predators.
Columbus finished 7-1-0 to set a team record for most preseason wins. Nashville was 3-3-0.
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