"We're going to play every game like this, no matter what," said Quick, who leads the league in postseason goals-against average (1.50) and save percentage (.948). "It doesn't matter how many games it takes, especially against that team. We're fortunate to move forward."
The Kings will face Chicago or Detroit when they attempt to reach the Stanley Cup finals for the third time. The Blackhawks will host the Red Wings in Game 7 on Wednesday night.
Quick couldn't do it all by himself, and he got help from a familiar big-game source: Williams scored on a power-play tap-in and a one-timer, putting the Kings on top to stay. The veteran wing came in with an eight-game goal-scoring drought, but the two-time Stanley Cup winner has scored nine points in his four career appearances in a Game 7.
"I certainly enjoy pressure situations," said Williams, whose goals came 2:57 apart. "I know everyone in this dressing room does. We pride ourselves on being a team that, push comes to shove, we're going to get it done. We've been through it before, and we know we can do it."
The home team won all seven games in the series, as did the team that scored first. The fifth-seeded Kings barely rode their home-ice advantage to victory in their first potential elimination game in the last two years.
"They were as good as us," Los Angeles coach Darryl Sutter said. "We just scored."
Antti Niemi stopped 16 shots for the Sharks, who fell just short of their third trip to the conference finals in four years. Even during a year of roster turnover and significant change, sixth-seeded San Jose remained a serious contender in its ninth straight playoff appearance.
"We thought we could come in here and steal a game," Thornton said. "We were just having so much fun. It's disappointing that it has to end, because we were really enjoying this. It's a tough way to finish."
Los Angeles has won eight straight home playoff games, dating to last season's Stanley Cup clincher, but this one might have been the toughest. San Jose pressed the action throughout the third period after Williams' back-to-back goals put the Sharks in a mid-game hole, but Quick and the Kings' defense hung on for a win in Los Angeles' first Game 7 at home since 1989.
"We had a bunch of chances in the third," Sharks forward Logan Couture said. "That's what teams do when they move on: They score on those chances they get. They did it, and we didn't."
After a scoreless first period in Game 7, featuring plenty of near-miss chances but just eight combined shots, the Sharks again came out aggressively in the second. San Jose held the Kings without a shot for nearly 19 consecutive minutes.
But the Kings finally broke through after San Jose's Brent Burns took an interference penalty near Los Angeles' net. Williams got the puck to the post and hacked at it until it slid behind Niemi for his first goal since Game 4 of the first round.
Williams, who had just two assists in the previous eight games, has been candid about his line's offensive struggles during this postseason, saying the Kings' top scorers had to get better for Los Angeles to advance. So he did it again 2:57 later, taking a cross-ice pass from Anze Kopitar and beating Niemi from short range with a one-timer.
Niemi kept the Sharks in it with two stunning saves, preventing a natural hat trick by Williams several minutes before stopping Brad Richardson's one-timer. Niemi made another enormous save during 4-on-4 play early in the third, stopping Jeff Carter on a breakaway.
Boyle ended Quick's bid for his third shutout of the series with a long shot through traffic with 14:34 to play, giving the defenseman his third goal of the postseason.
"We probably made one more mistake than they did, and we couldn't find a way to get another puck by Quick," McLellan said. "We would love to go back and play Game 2 over again, the last four or five minutes. That's probably one that we needed and didn't get."
The Sharks missed either team's best chance to win a road game 12 days earlier, giving up two power-play goals in the final minutes of a 4-3 loss in Game 2. The clubs were similarly equal in the regular season, when the Kings' 3-2 home victory over San Jose in the finale pushed fifth-seeded Los Angeles ahead of the Sharks.
That eventually led to the Kings starting a playoff series at home for the first time since 1992, but the uncanny home-ice advantage held: The home team has won 16 of these California rivals' 17 meetings in the past two seasons.
With one more postseason test, the Kings passed.
"It comes from the hunger of winning one and having that drive for another one," Williams said. "You don't want anyone else to raise the Cup but you."