Nashville beat St. Louis for the sixth time this season and 14th straight overall. The first five victories this season came by one goal, including three in overtime.
The Predators rallied from a 2-1 deficit after the first period with goals from Sullivan and Jason Arnott in the first 5:45 of the second. Sullivan scored on a two-man advantage - the game's only power-play goal - 2:15 into the period. He took a cross-ice pass from Paul Kariya and easily put the puck past goalie Curtis Sanford to tie the score at 2.
Arnott, who got an assist on Sullivan's goal, gave the Predators the lead for good after he tapped in his 17th goal of the year. Nashville has won 10 of its last 11.
Erat got his first after throwing an easy shot past Sanford with one minute left in the second and added his second late in the third to put the game away. Sullivan scored an empty-net goal for the final score.
The game continued to be a physical battle the two teams have had for most of their games this season. The Blues received the only penalty in a first period that was filled with hard hits and led to a second period that saw 16 penalty minutes.
The teams traded quick scores in the first. Scott Hartnell scored his team-high 19th to give Nashville a 1-0 lead only to see the Blues tie the score 13 seconds later on Lee Stempniak's 16th of the season. Hartnell got past Eric Brewer to tap it past goalie Curtis Sanford off assists from Shea Weber and Ryan Suter.
The public address announcer didn't have time to recap the score before the Blues struck back. As they went into the Nashville zone, Stempniak passed the puck to Jay McClement who returned it to a wide-open Stempniak who knocked in the tying goal.
Notes: Nashville recalled D Mikko Lehtonen and reassigned F Alexander Radulov to Milwaukee of the AHL. ... The Blues announced a crowd of 16,346, marking the first time since the lockout they have had at least 16,000 in three consecutive games.