After the Sharks allowed the tying goal at 12:56 in the third, Joe Pavelski scored at 17:20 to lift San Jose to victory and a 2-0 series lead over Nashville.
Joe Thornton added an empty-net goal in the final minute to seal the Sharks' 3-2 win Sunday night.
The Predators added a goal with 3.6 second left to make the final score closer.
Logan Couture got the Sharks on the board at 18:36 in the second period.
Martin Jones had made 30 saves before Mattias Ekholm beat him to tie the game 1-1.
The Western Conference Second Round series shifts to Nashville, where Game 3 is Tuesday night.