The Predators have won six of seven, while the Blues have dropped three of four.
Chris Porter had the lone goal for St. Louis.
It was the fourth meeting of the season between the Central Division rivals, with Nashville winning all four matchups so far. The Predators are 12-2-2 against the Central this season.
Erat scored the game's first goal at 6:59 of the opening period. With the Predators on the power play, Erat moved away from the right point before firing a slap shot over the glove of St. Louis goaltender Jaroslav Halak.
Fisher doubled the Nashville lead with 7:30 to go in the first. Sergei Kostitsyn had the puck behind the St. Louis goal and found Fisher in the low slot. After a quick toe-drag, Fisher beat Halak with a wrist shot high to the stick side.
Fisher has six goals in his last five games.
One night after recording his fifth shutout of the season, Halak was again strong in goal for St. Louis in making 34 saves. He is now 12-2-3 in his last 17 starts.
Porter cut the deficit to 2-1 at 4:01 of the third period. Inside the Nashville zone, Porter picked the pocket of Predators rookie defenseman Roman Josi in the slot. After the takeaway from Josi, Porter fired a wrist shot by a surprised Rinne.
With intense St. Louis pressure in the late minutes, Rinne showed why he is the league's reigning Third Star of the month.
Rinne twice denied defenseman Kris Russell late in the third, first with 8:42 remaining and then again 5 seconds later. On the second save, Rinne dove to his left after being knocked out of position making the first save on Russell.
Kostitsyn concluded the game's scoring on an empty-netter with 22.1 remaining.
Notes: St. Louis C Jason Arnott missed the game with a shoulder injury. Arnott, who captained the Predators for three seasons, has missed just two games this season, both in Nashville. ... Nashville RW Brian McGrattan played after being a healthy scratch for six consecutive games. ... Predators RW Matt Halischuk played in his 100th career NHL game.