Quick recorded his second shutout of the post-season as the defending Stanley Cup champion Kings won their fifth straight game. They won four consecutive contests against St Louis in the first round after falling into a 2-0 hole.
Game Two of the best-of-seven set is also in Los Angeles on Thursday.
In the first standoff between the Pacific Division rivals, Slava Voynov scored in the first period and Mike Richards netted in the second for the Kings, who needed very little offense to seal the victory.
Los Angeles took just 20 shots against Antti Niemi, who made 18 stops.
After running through the playoffs as an eighth seed a year ago, the Kings have home ice advantage in a playoff series for the first time in 21 years.
Fifth seeded Los Angeles has been especially lethal at the Staples Center, where they have won 11 straight.
Conn Smythe Trophy winner Quick was at his best in the opener as his team handed the Sharks their first loss of the playoffs.
San Jose swept Vancouver in the first round.
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