Nashville, down 3-1 with time running out in regulation, scored twice in the final 1:36 to force overtime.
Patric Hornqvist brought Nashville within one and Sergei Kostitsyn tied it with 13 seconds left in the third. Kostitsyn's goal came with Columbus' Samuel Pahlsson in the penalty box for cross-checking.
The Predators ended a two-game skid.
The stunning setback added to a season of woes for the Blue Jackets, who have eight victories in 29 games.
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