Pekka Rinne made 18 of his 41 saves in the 1.
Rinne is in the midst of a personal 11-game win streak and hasn't lost since January 5. He has allowed two goals or less in all but one contest over his current win streak.
Chris Porter scored the lone goal for the Blues, who have lost three of four and now sit one point back of Nashville for second place in the Central Division.
Jaroslav Halak stopped 34-of-36 shots in the loss.
"Obviously, Rinne played extremely well and made some big saves, but I think the thing we seemed to do in stretches was to get away from our game and try to find some cute way of passing it around him and that's exactly what they want," Blues forward Jamie Langenbrunner said.
The Predators scored a power-play goal at the 6:59 mark of the first period. Erat's blast from the right point got past Halak.
Fisher made it a 2-0 game at the 12:30 mark. Kostitsyn carried the puck along the goal line before finding Fisher in front. Fisher chipped the disc past Halak to complete the play.
Rinne stopped 16 shots over the first 20 minutes. He made seven saves in a scoreless middle stanza.
St. Louis finally beat Rinne at the 4:01 mark of the third. Porter stole the puck away from Roman Josi at the high slot and quickly fired a shot past Rinne.
Rinne made two amazing saves against Kris Russell with less than nine minutes to play. On the second save, Rinne made an acrobatic dive to his left.
"There's not too many goaltenders in the league who would make that save," Predators head coach Barry Trotz said. "That's why I keep saying, 'He's the best one.'"
Kostitsyn scored an empty-net goal with 23 seconds left to seal the victory.
The Predators improved to 12-2-2 against the Central this season...Halak is 12-2-3 in his last 17 starts...The Blues started a three-game road trip on Saturday...Blues forward Jason Arnott (shoulder) missed the game.