Justin Williams and Anze Kopitar each notched an assist for the eighth-seeded Kings, who own a 3-0 series lead for the first time in franchise history. They will try to complete the sweep at home on Wednesday.
Brown, who drew the ire of the Canucks for a hit on Henrik Sedin early in the second period, gave Quick all the offensive support he needed with his fourth goal of the series.
Williams' shot from the top of the right faceoff circle was stopped by Cory Schneider. But the rebound went right to Brown, and the Kings' captain buried it from the bottom of the left circle for a 1-0 advantage.
Quick turned aside 11 shots in the first period, 14 in the second and 16 in the third for his second career postseason shutout. The 26-year-old led the NHL with 10 regular-season shutouts.
