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.
"I didn't think we tested him a lot tonight," San Jose coach Todd McLellan said. "There are a number of goalies in the league that could have performed that way tonight."
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 in Game 5. 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.
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