Artem Anisimov and Nick Foligno scored in regulation for the Blue Jackets, who finished last in the Western Conference in the 2011-12 season.
Sergei Bobrovsky made 32 saves to earn the win for Columbus.
Ryan Ellis and Martin Erat scored for Predators, who are coming off last season's second consecutive second-round playoff exit.
Pekka Rinne turned aside 26 shots for Nashville.
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