Lindback made 27 saves over the final two periods to hand the Red Wings their third straight loss, their longest skid this season.
J.P. Dumont scored unassisted to give Nashville a 3-1 lead with 5:23 to play and Johan Franzen brought Detroit within one by finally getting a shot past Lindback with 1:33 to go.
The Predators survived to win in Detroit for the first time in two seasons.
Jimmy Howard stopped 21-of-24 shots for the Red Wings.
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