Rinne was especially busy in the third period when the Flames outshot Nashville 14-2. The Finnish goalie held on, however, for his 21st career whitewash.
Niclas Bergfors gave the Predators a 1-0 lead early in the second period when he snapped a pass from Jack Hillen into the net during a 3-on-2 rush.
Sergei Kostitsyn made it 2-0 in the third, tipping in a cross-crease pass from Craig Smith.
Miikka Kiprusoff stopped 12-of-14 shots for the Flames, who fell to 2-4-1 to start the season.
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