Alexander Frolov had two goals and an assist, and Lubomir Visnovski had a goal and an assist to help the Kings win for only the fourth time in their last 17 games. Los Angeles outshot San Jose 34-18.
Milan Michalek and Joe Thornton scored for the Sharks, who were playing at Staples Center for the second time in five nights after beating the Kings 7-3 last Thursday.
Brown got a cross-ice pass from rookie Anze Kopitar and beat Vesa Toskala to the stick side from short range for his third goal of the season, 37 seconds after referee Mick McGeough gave Steve Bernier a holding-the-stick penalty. Toskala came in 4-0 lifetime against the Kings with a 2.00 goals-against average.
Frolov scored into an empty net with 23 seconds to play.