The Sharks led 1-0 for most of the game, thanks to Logan Couture's shorthanded goal less than 6 minutes into the contest.
Craig Smith finally put the Predators on the scoreboard with 7 minutes remaining, sending a back-hander into the net through traffic while San Jose's Ryane Clowe was serving a penalty for unsportsmanlike conduct.
Pavelski answered 57 seconds later, stuffing a puck past Nashville's Pekka Rinne on a wraparound move.
Pavelski added an empty-netter and Antti Niemi stopped 19-of-20 shots for the Sharks, who notched their third straight win.
Rinne finished with 33 saves for Nashville, which fell to 0-2-1 at home.