Erat's unassisted backhander at 11:45 proved to be the game-winner and Legwand knocked in a power-play score at 19:43 to give Nashville its first win of the season and hand the Wild its first loss.
Erat scored on a breakaway as Wild goaltender Niklas Backstrom skated past the faceoff circle but could not control the rolling puck, leaving it for Erat.
Chris Mason stopped 29 shots for the Predators, who had lost their first two games of the late-starting season. Minnesota's Backstrom tallied 23 saves in the loss.
Nick Spaling scored the other Nashville goal on a wrist shot at 16:31, some 10 minutes after Danny Heatley opened the scoring for Minnesota with a wrist shot from the blue line that sailed through traffic into the net.