The Sharks, who defeated the Kings 6-3 in Game 5 at Staples Center on Friday, face the winner of the first-round series between the Anaheim Ducks and Nashville Predators, where the Ducks lead 3-2.
San Jose avenged a bitter first-round loss to Los Angeles in 2014, when they took a 3-0 series lead but dropped the final four games. The Kings also beat the Sharks in a second-round series in 2013 that went seven games.
"It feels great," Sharks first-year coach Peter DeBoer said Friday. "I haven't been around here for some of the stuff that's gone on in the past.