Anze Kopitar scored, then Jarrett Stoll got a short-handed goal. There was another score in the final second of the second period.
Once the Los Angeles Kings got going, the host Chicago Blackhawks just couldn't stop them.
Brown converted his own rebound with 1:27 remaining, and the Kings scored all their goals in the final two periods of a 5-4 victory on Monday night.
"It was just a team effort," Kopitar said. "Going into the game, we knew we had to get 20 guys on board. We just stuck with it."
It was Los Angeles' highest-scoring game since a 5-2 victory over the Sharks on March 16 and came on the heels of consecutive shutout losses to Dallas and Vancouver. The scoreless stretch reached 150 minutes, 35 seconds before Kopitar picked up his 10th goal of the season at 4:21 in the second.
"We didn't respond to the challenge that was there tonight, and I was disappointed with how we played and what we gave them," Blackhawks coach Joel Quenneville said.
The Blackhawks were without right wing Marian Hossa for the second straight game due to an upper-body injury.
Wild 7, Stars: Zach Parise scored two goals and added an assist, and Minnesota extended its winning streak to six games with a victory in Dallas.
Both of Parise's goals came on bounces that barely made it over the goal line as Minnesota won for the first time in Dallas since March 21, 2003, snapping a 16-game losing streak in Dallas (0-11-5).
With the game tied 4-4 in the third period, the Wild got a short-handed goal from Kyle Brodziak at 12:38. Dany Heatley added an insurance goal with 1:28 remaining, and Pierre-Marc Bouchard added an empty-netter with 16 seconds left.
Red Wings 3, Coyotes 2: Pavel Datsyuk scored Detroit's second power-play goal in the third period and had an assist to help the Red Wings beat host Phoenix.
Predators 3, Oilers 2: Sergei Kostitsyn had a goal and an assist to lead host Nashville over Edmonton.
Lightning: Tampa Bay Lightning hired Jon Cooper as its coach. Cooper had been coaching Syracuse of the AHL, Tampa Bay's top minor league affiliate. He replaces Guy Boucher, who was fired Sunday.
Hurricanes: Carolina and Alexander Semin agreed to a five-year contract extension that will pay him $7 million per season and keep him with the team through 2017-18.