Pavel Datsyuk had a goal and an assist and Johan Franzen also scored for Detroit, which lost its third straight and second in a row in regulation. Jimmy Howard stopped 21 saves.
Dumont gave Nashville a 3-1 lead with 5:23 left on a wrist shot from the right circle on a 2-on-1.
Franzen cut it to a goal with 1:33 remaining with his 13th of season.
Datsyuk's short-handed goal with 6:56 left in the second period cut the Predators' lead to 2-1. He put in his own rebound by swatting the puck out of the air for his ninth goal.
Erat was credited with the goal that gave Nashville a 2-0 lead just 49 seconds into the second when the rebound of his shot bounced in off Red Wings defenseman Jonathan Ericsson.
The Predators' Kevin Klein swept a rolling puck off the goal line behind Lindback with just over 11 minutes left in the middle period.
Nashville opened the scoring with 32 seconds left in the first period on Wilson's sixth goal. He tapped Cal O'Reilly's pass into an empty net from in front. The play was the result of Franzen's turnover just inside the Predators' blue line.
NOTES: Nashville C David Legwand returned after missing nine games because of a lower-body injury. He was born in Detroit. ... Detroit sent D Jakub Kindl to its AHL affiliate in Grand Rapids for a two-week conditioning stint. ... Erat went to the locker room with 8:55 left in the second period after getting an accidental stick in the face from Tomas Holmstrom. Erat was face down on the ice before being attended to by the trainer. Holmstrom received a double minor for high-sticking.