Brown scored with 35 seconds left in overtime and the Kings beat the Boston Bruins 3-2 on Thursday night as the struggling Eastern Conference leaders squandered a 2-0 lead.
"It's a huge win for us," Brown said. "We've shown we could come back many times this year and this is just another one, but it just happened to be against one of the better teams in the league."
The Bruins are 6-9-4 in their last 19 games after going 39-8-6 in their first 53.
"We're going to have to start outworking other teams from start to finish like we were earlier in the season," Boston coach Claude Julien said, "and your best players are going to have to find their game and be the best they can be in order for us to get out of it."
The Kings remained 13th in the Western Conference but within striking distance of the eighth and final playoff spot with 12 games left -- the next five on the road.
"To start this off with a win in Boston," Los Angeles coach Terry Murray said, "was very important to have that kind of feeling and build some momentum here at the start for the rest of the trip."
They were 3-6-1 in their 10 games before Thursday, but four of those losses were by one goal.
"We weren't in awe of the Boston Bruins," Murray said. "We know they're a great team but we know we have to go out and play the game, so playing with composure and playing the right way was what was talked about at the start."
The Bruins seem to have lost their aura of dominance, something goalie Tim Thomas has seen during the current slump.
"Whether we're on the road or at home, teams are coming up against us and it's almost like they've got the upper hand already," Thomas said, "because they're the more confident team."
A victory would have built the Bruins' confidence -- and clinched a playoff berth -- but now they await Sunday's game against New Jersey, which trails them by five points but has played two fewer games.
"We know what's at stake on Sunday and we've got to have a big win," said Mark Recchi, whose second period goal gave Boston a 2-0 lead.
But Michal Handzus scored on a power play for Los Angeles with 10:10 left in the third period, and rookie defenseman Drew Doughty tied it with 1:36 remaining in regulation.
The Kings began their winning play from their own end.
Brown passed the puck and Thomas made a kick save on Sean O'Donnell's shot, but had little chance to stop Brown, who scored his 24th goal.
"I just dished it wide and cut for the net," Brown said, "and there was a rebound sitting for me."
Matt Hunwick, a healthy scratch the last five games, gave Boston a 1-0 lead at 14:41 of the first period with his sixth goal of the season.
Recchi scored at 3:48 of the second period, his 17th goal of the season and his fourth since being obtained from Tampa Bay on March 4.
But the Bruins failed to capitalize on two power plays in the second period and the momentum began to shift even before the Kings scored.
"We left them in the game and kind of made believers out of them," Thomas said.
Handzus began the comeback with a power-play goal when he converted a rebound from the side of the net on a shot by Teddy Purcell. Handzus' 16th goal of the season came with 11 seconds left in a penalty to Aaron Ward.
The Kings tied it on Doughty's fifth goal. Wayne Simmonds' shot from just in front of Thomas hit the post to the goalie's left and ricocheted to Doughty, who knocked the puck in from the other corner of the net.
"It's definitely special," Doughty said. "They're the best team in the Eastern Conference. To be able to play with them like that and outshoot them and end up winning the game in overtime just gives us a lot of confidence."
Los Angeles outshot Boston 38-26, including 3-0 in overtime. ... The Bruins are in the midst of a slow stretch with two games in 12 days. They have five days off after facing the Devils on Sunday. "You don't get this [rest] very often at this time of the year and I think we've got to take advantage of it and then try and get on a big roll right at the end," Recchi said. ... The Kings outshot the Bruins 8-1 at the start of the game and 16-7 after the second period.