With the victory, Nashville rose to 80 points, tying Vancouver for the eighth playoff spot in the Western Conference.
Center Rich Peverley's third goal this season at 6:10 of the second period broke a 1-1 tie and was the game-winner.
He scored when Detroit goaltender Chris Osgood mishandled the puck behind his own net.
Niklas Kronwall scored the lone goal while Osgood was beaten twice on 26 shots for the Red Wings, who already have clinched the Central Division crown and are bidding to clinch the top seed in the Western Conference.
Red Wings center Pavel Datsyuk had an eight-game point streak snapped.
The attendance at Detroit's Joe Louis Arena was 20,066.