Rinne was working on a shutout until San Jose's Martin Havlat scored on a power play with 6 1/2 minutes remaining in regulation to tie it up at 1-1.
Sergei Kostitsyn scored in regulation for Nashville, which notched a second straight win.
Niemi made 23 stops for the Sharks, whose seven-game winning streak to start the season was snapped.
Aaron Carter is still in love with Hilary Duff
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