Chuck Kobasew scored late for Minnesota, which lost for the second time in three games and was booed off the ice after the second period and the game. The Wild are 3-6-1 in their last 10 home games.
Rinne won for the first time in four starts since returning from a left knee injury that sidelined him for eight games. He made two of his best saves during a third-period penalty kill, hugging the post to stop Martin Havlat from in close and squaring up to deny Matt Cullen on a slap shot from the left circle.
Rinne also robbed Havlat in front with a right pad save midway through the first period, and stopped Mikko Koivu's tip late in the second.
For the first time in seven games, Nashville scored first when Franson beat a screened Niklas Backstrom with a slap shot from the blue line 4:37 into the game.
Ward and Kostitsyn scored empty-net goals.
Backstrom got the start despite a scare practice Thursday when he was run into by defenseman Marco Scandella and fell to the ice grabbing his knee. Backstrom stopped 28 shots.
Kobasew scored with 1:54 remaining, tipping in a shot from Havlat.
- Wild RW Cal Clutterbuck, the NHL leader with 165 hits, missed the game because of what the team called a "nagging injury." He played in the Wild's first 36 games of the season.
- RW Marek Svatos made his debut for the Predators. He was claimed off waivers from St. Louis on Wednesday, after signing with the Blues Tuesday. Svatos, who played the last six seasons with Colorado, started the season in Russia's Kontinental Hockey League.
- Nashville C David Legwand, who had missed nine straight games and played just once since Nov. 18 because of a lower-body injury, had two assists.