Nashville has won five of seven, while Toronto has dropped five of its last six.
Ryan Suter and Matt Halischuk scored the other Nashville goals. John-Michael Liles
replied for Toronto.
The Predators' Sergei Kostitsyn had three assists, tying his career high for assists and points in a game.
Erat gave the Predators a 1-0 lead just 5:48 into the game with his fourth goal in four games.
From the goal-line just to the right of the Toronto net, Mike Fisher sent the puck toward goalie Ben Scrivens
. Erat got the puck, and beat Scrivens with a wrist shot to the short side.
Liles tied it at 10:36 of the second.
With the Maple Leafs on a power play and both teams attempting to change lines, Liles picked up the puck at centre ice and drove into the Nashville zone on the right side. Liles beat Rinne with a wrist shot from the circle.
Nashville regained the lead less than two minutes later when Suter's shot from the left side through traffic beat a screened Scrivens.
Suter scored his fourth of the season, matching his total of each of the previous two seasons.
Erat gave Nashville a 3-1 lead at 2:05 of the third, capitalizing on a cross-ice pass from Fisher with the Predators on a 2-on-1 break.
Halischuk added an empty-net goal to seal the win. NOTES:
Nashville, in its 13th NHL season, hosted Toronto for just the fourth time. ... Suter was one of three Madison, Wis., natives who played in the game along with Nashville C Craig Smith and Toronto RW Phil Kessel
. ... Kostitsyn hadn't recorded a point since Oct. 27. ... Kessel had his four game point streak snapped. ... Rinne has started all but one of Nashville's games this season.