Magnus Paajarvi had the other goal for the Blues, who have won all four of their games against Nashville this season.
Ott's assist was his first point as a Blue.
Nashville drew even at 10:28 of the first on Spaling's 11th goal of the season.
From the right half boards, Patric Hornqvist sent a pass in front, where Spaling tipped the puck high over Miller's right shoulder.
St. Louis regained the lead at 8:18 of the second on Paajarvi's sixth of the season.
Paajarvi took a pass from Roman Polak in the neutral zone and then skated into the Nashville zone on the right side, where he cut into the right faceoff circle and beat Rinne with a quick wrist shot.
Alexander Steen was awarded a penalty shot at 15:27 of the second period after being fouled from behind on a breakaway, but Rinne gloved down Steen's wrist shot from the right side.
Steen has converted one of two penalty shot attempts this season, while Rinne has turned aside the two that he has faced.
NOTES: Hornqvist's assist was the 100th of his career. . Nashville C Mike Fisher has points in five consecutive games, equaling a season high. . The Blues are 34-1-4 when scoring first this season