Chris Stewart and Vladimir Sobotka scored for St. Louis in regulation, while Roman Josi and Colin Wilson had the goals for Nashville.
Jaroslav Halak made 25 saves for the Blues, then was perfect in the shootout, stopping Wilson and Martin Erat.
Pekka Rinne stopped 22 shots for the Predators.
Stewart got the only goal of the opening period, then Josi and Wilson gave Nashville a 2-1 lead. Just 34 seconds after Wilson's goal, Sobotka tied it, and the third period was scoreless.
Stewart opened the scoring after a short-range shot by Jason Arnott bounced off the left goal post. Stewart skated into the slot from the right and put the puck in from just above the crease with Rinne out of position.
Josi skated in from low in the slot and fired a wrist shot over the right shoulder of Halak to tie the game. Wilson gave the Predators a 2-1 lead by beating Halak to his stick side with a backhander in front of the net.
The lead was short-lived. The Blues responded when Sobotka emerged from a crowd in front of the net and shot a backhander high over Rinne.
NOTES: The Predators have not allowed a power-play goal for five straight games. ...The Blues have stopped 17 of 20 power-play attempts by the Predators in the last 10 games in the series. ...Wilson is only four points away from tying his career high in points. ... St. Louis has points in eight of the last 10 games with the Predators.