Patrick O'Sullivan, Alexander Frolov and Jarret Stoll each lit the lamp for the Kings, who have won three in a row for the first time since a season-best four-game winning streak from November 6-13. Kyle Quincey had a pair of helpers in the win and Jonathan Quick stopped 31-of-33 shots for the win.
Patrick Sharp and Dave Bolland scored for the Blackhawks, who have lost three of four overall. Brian Campbell had a pair of assists and Cristobal Huet gave up four goals on 25 shots.
The Kings got on the board at the 14:47 mark of the first period via a power- play tally from Brown. Off assists from Anze Kopitar and Quincey, Brown's wrist shot found its way past Huet and into the back of the net.
Less than two minutes later, Kyle Calder gained control of the puck behind the net and fed it to Stoll, stationed in front of the cage. His wrister also beat Huet for a 2-0 LA lead with 3:28 left in the period.
The Kings took a 3-0 lead early in the second period as Quick made a save and relayed the puck to O'Sullivan, who skated down the right side of the ice. It was a one-on-one and his snap shot beat Huet to the far side of the net for a short-handed goal.
"We wanted to get a good start, get two points against a good hockey club," said Kings head coach Terry Murray. "It wasn't pretty all of the time but the bottom line is that we got two points against a really good team."
Chicago got on the board at the 7:31 mark of the third period. Campbell, at the back right corner of the ice, slid a one-timer to the right circle for Bolland. His slapper beat Quick above the glove for a 3-1 game.
However, LA got the goal back just 37 seconds later on Frolov's backhander.
"I think L.A. is a lot better than what people give them credit for," said Campbell. "They are a good hockey team and obviously played us pretty well last time. We've got to find a way to be better."
Sharp's slap-shot tally brought the Blackhawks within 4-2 with 8:28 left in the contest.
Brown recorded an empty-net goal with 41 ticks remaining to account for the final margin.