Ross Colton and Nick Perbix scored, and Roman Josi had two assists for the Predators (8-4-5). Juuse Saros made 24 saves.
Jimmy Snuggerud scored and Joel Hofer made 26 saves for the Blues (7-8-2), who lost their third straight (0-2-1).
Snuggerud's power-play goal gave the Blues a 1-0 lead at 13:07 of the first period. Philip Broberg received a pass at the point from Robert Thomas and sent the puck to the top of the left circle, where Snuggerud beat Saros with a snap shot.
Stamkos answered on the man-advantage to tie it 1-1 at 16:07. He wristed a rebound from the left side into the open net with Hofer dealing with traffic in front of the net. It was his 248th career power-play goal to pass Luc Robitaille for sole possession of fifth in NHL history.
Colton put the Predators ahead 2-1 at 9:02 of the second period. After being denied on a tip-in attempt 20 seconds earlier, he collected a feed in the high slot from Jack Drury and used a screen from Adam Edstrom to beat Hofer.
Perbix scored an empty-net goal with 1:29 remaining in the game for the 3-1 final.
