The Blues lost for the sixth time in seven games and fell into last place in the Central Division, one point behind Nashville.
Tootoo put the Predators in front by scoring on a slapshot with 3:43 to play in the third. Legwand added an empty netter with 7 seconds to play.
The only St. Louis goal came from Brad Boyes 2:03 into the game. Patric Hornqvist tied it in the second period.
Pekka Rinne made 31 saves to get the victory. Rinne has won five of his last six starts.
Chris Mason allowed two goals on 36 shots.
This was the second contest in a six-game St. Louis homestand. Nashville wrapped up a four-game road trip, on which the Predators went 2-2.