Quick made a handful of spectacular saves down the stretch as the Sharks pressed for equalizer, but withstood the assault to preserve the Kings' victory in Game 7 of their Western Conference semifinal series.
Justin Williams scored goals less than 3 minutes apart in the second period with Slava Voynov assisting on both tallies as the defending NHL champions advanced to the conference finals for the second straight year with their seventh consecutive home win.
The fifth-seeded Kings now await the winner of Wednesday's Game 7 against the Chicago Blackhawks and Detroit Red Wings in the other West semifinal series.
Dan Boyle's goal 5 1/2 minutes into the final frame drew the Sharks to within one, but they could get no closer.
Antti Niemi turned aside 16-of-18 shots for sixth-seeded San Jose, which was unable to record a road win the series.