LOS ANGELES — Jonathan Quick saved his best save for the final minute, sliding deftly across his crease and snagging Joe Pavelski’s shot from point-blank range to the grateful gasps of the Los Angeles Kings’ sellout crowd.

Quick’s imposing postseason presence only appears to be growing, and the San Jose Sharks are running out of time to figure him out.

Quick made 24 saves in his seventh career playoff shutout, and the Kings moved to the brink of their second straight trip to the Western Conference finals with a 3-0 victory in Game 5 on Thursday night.

Anze Kopitar and Slava Voynov scored, and Jeff Carter added an empty-net goal as the defending Stanley Cup champions won their 13th consecutive home game in dominant fashion, claiming a 3-2 series lead.

Quick won his 27th postseason game, taking sole possession of the franchise record from Kelly Hrudey. The Conn Smythe Trophy winner shut out the Sharks for the second time in the series, yet Quick scoffed at any suggestion he’s responsible for the Kings’ abrupt reversal of this series’ momentum after the Sharks appeared to take control in San Jose.

“We came out with a purpose,” said Quick, who has stopped 313 of 330 shots in the postseason. “We knew what was on the line tonight, and I’m lucky to play with guys who care so much about winning. Top to bottom, I thought everybody played well, but it’s just three wins. We know that doesn’t mean anything.”

Game 6 is Sunday night at the Shark Tank.

Quick has three shutouts in this postseason alone, adding to his club record of seven playoff shutouts, yet nobody thought this latest zero was his best number of the postseason. The Sharks lamented their lackluster effort, particularly from the star players whose dominance had allowed San Jose to even the series with two straight wins and three straight games of largely superior play.

“They tested us for the first four games, and I like the way we responded,” Kings defenseman Matt Greene said.

Antti Niemi stopped 26 shots for the Sharks, who have played more than 96 minutes without a goal since they appeared to be taking control of the series midway through Game 4.

“We’ve got to score. It’s the playoffs,” Sharks forward Logan Couture said. “We had enough chances to win tonight, but we have to start bearing down and scoring some goals. We weren’t there at the start. I don’t even think we were good at any point in this game tonight. Our power play was brutal.”

The home team has won every game in the series, and the Kings remained unbeaten at Staples Center since March 23. Los Angeles, 25-4-1 at home this season, has won seven straight home playoff games dating to last season’s Stanley Cup clincher against New Jersey.

After getting soundly outplayed to start each of the past three games, the Kings met the Sharks’ tempo and urgency from the beginning in Game 5. The Kings sharpened their physical game, outmuscling and outhitting the Sharks from the opening faceoff.

Kopitar finally collected a reward late in the second period, tapping in a loose puck after a sustained stretch of pressure on Niemi. Voynov then scored 3 seconds after a penalty expired early in the third, firing home his fourth goal in nine games.

Quick finished up from there, stopping Pavelski a few seconds before Carter wrapped it up with an empty-netter.

“We were going at them pretty hard, and got sustained pressure for long periods of time,” said Kopitar, who got just his second goal of the postseason. “There’s nothing new to say about (Quick). He gives us a chance every night. He makes every save he should, and a few he shouldn’t, every time.”

San Jose substantially outplayed the Kings in the first period of the past three games, and Los Angeles cited a strong start as its key priority for Game 5. The Kings got it, albeit in a scoreless first period, outshooting the Sharks 9-6 while playing a punishing physical game that slowed down Joe Thornton and hampered San Jose’s relentless speed.

“The power play looked like it was a little bit nervous for some reason,” Thornton said. “I don’t know why. It looks like we just didn’t have some poise on the power play. If our power play is going good, you can see guys get some confidence. When it doesn’t, you see guys kind of get down, and that’s what happened tonight.”

The Sharks played roughly 17 minutes without a shot into the second period, but the Kings couldn’t cash in several scoring chances in front of Niemi, including golden opportunities for Mike Richards and Justin Williams.

San Jose got several chances of its own, notably with a 2-on-1 break for Patrick Marleau and Couture, but Quick kept everything out of his net.

Niemi made a spectacular save on Carter’s wraparound chance late in the second period, but that play led to a long stretch of uninterrupted pressure and the go-ahead goal. Kopitar’s tap-in included assists for Williams and Kyle Clifford, who replaced Dustin Brown on the Kopitar-Williams line for Game 5.

The Kings hope a goal will jump-start Kopitar, who didn’t score a goal in the Kings’ final 16 regular-season games. The Slovenian center was the postseason’s co-scoring leader last summer with 20 points in 20 games.

The Kings scored again when Trevor Lewis won a faceoff against Thornton, who has dominated the circle in the series. Lewis, who scored the winning power-play goal late in Game 2, got the puck to Voynov for a long shot through traffic immediately after a power play ended, and the Siberian defenseman matched Carter for the team lead at the time with his fourth goal of the playoffs.

The power play resulted from a goalie interference penalty against TJ Galiardi, who drew the Kings’ ire Wednesday by claiming Quick embellishes contact with opponents to draw undeserved penalties.

“Well, he got his call tonight, so I’ve got to be better,” Galiardi said. “I’ve just got to know that if there’s any contact at all, they’re going to call it. They made us pay right after the penalty expired, so that’s on me.”

NOTES: After sitting out earlier in the postseason with an injured left ankle, Jason Demers got his first action of the postseason for San Jose, which sat LW Tim Kennedy to make room. Demers, normally a defenseman, usually played forward. The Sharks are playing without injured forwards Marty Havlat and Adam Burish. … Los Angeles dressed the same lineup as in Game 4, although coach Darryl Sutter shuffled his lines. … Tom Cruise and producer Jerry Bruckheimer watched the game from seats on the glass.