Jared Boll scored his first NHL goal in 20 months, and Rickard Rakell had a goal and an assist for the Ducks (6-6-3), who lost goalie John Gibson to an upper-body injury in the third period.
Los Angeles trailed 2-0 in the first period and 3-1 in the second before tying the game 3-3 on a power-play goal by Brown at 5:49 of the third.
The Kings were 1-for-7 on the power play. Brown scored on the first of four opportunities in the third period.
"The emotion got high in the third period," Ducks defenseman Francois Beauchemin said. "We want to be physical at the same time, so we will take penalties, but we have to limit those, for sure."
Brown appeared to give the Kings a 4-3 lead at 10:15, but Ducks coach Randy Carlyle challenged, and video review showed Drew Doughty was offside prior to the goal.
Los Angeles forward Brooks Laich put in a rebound with 6:53 remaining, but the goal was immediately waved off because Gibson lost his mask making the initial save.
Gibson appeared to be hit in the head with a stick on the play. He was replaced by Ryan Miller, who made nine saves.
Rakell gave Anaheim a 3-1 lead when he scored his Ducks-leading sixth goal on a slap shot from just above the right face-off circle at 14:52 of the second period. Los Angeles coach John Stevens challenged the goal for interference against Quick, but video review showed defenseman Oscar Fantenberg caused Anaheim forward Corey Perry to contact the goalie.