Sergei Kostitsyn scored twice and captain Shea Weber added a goal for Nashville, which snapped a four-game losing streak.
Including a 3-0 home loss to Columbus on Friday, the Red Wings have been shut out in consecutive games.
Rinne was stellar in earning his third shutout of the season and 17th of his NHL career. After turning aside six Detroit shots in the first, he saw 12 shots in the second and 17 in the third.
Weber gave Nashville a 1-0 lead 3:18 into the game.
With the Predators on a power play, Weber carried the puck from the top of the right circle to the dot, where he sent a slap shot past goalie Joey MacDonald.
The Red Wings had an opportunity to tie it early in the second period when they had a two-man advantage for two minutes after Kostitsyn and Patric Hornqvist were given penalties at 44 seconds.
Kostitsyn's short-handed goal at 14:03 of the second period made it 2-0.
From deep inside the Nashville zone, Ryan Suter sent a long breakout pass to Kostitsyn at the Detroit blue line. Kostitsyn drove toward the net with defenseman Jakub Kindl on him. With just his right hand on his stick, Kostitsyn shoveled the puck toward the net. The puck ski-ramped up the stick of MacDonald and into the net.
With under three minutes remaining in the third, Kostitsyn scored his second of the game off of a pass from Marcel Goc. It was his 14th goal of the season.
Acquired by Nashville in an offseason trade with Montreal, Kostitsyn has already established career highs in goals and points.
Notes: LW Steve Sullivan returned to the Nashville lineup after missing 18 games with a lower-body injury. ... The Predators are 9-1 this season when Weber scores a goal. ... Detroit LW Jan Mursak left the game with an undisclosed lower-body injury and didn't return. ... MacDonald is 0-3 in his career against Nashville.