Meanwhile, the Calgary Flames have fallen as low in the standings as they can go.
Brown scored two goals, Jonathan Quick made 23 saves and the surging Kings beat Calgary 3-1 on Monday night for their second win over the Flames in three days.
Brown and Jarret Stoll scored first-period goals before Brown added an empty-netter for the defending Stanley Cup holders, who moved up to third place in the conference with their 11th win in 14 games. The victory wasn't exactly beautiful, but the Kings' workmanlike play and sturdy effort pleased their captain.
"When you win the Cup, you have a confidence in your group, because you've been there," Brown said. "It's just a matter of getting to work every day and doing things right, and we've been doing it lately."
Despite a rough third period dominated by Calgary, the champs finished their five-game homestand with four victories. With steadily improving play after a slow start to the season, Los Angeles trails only Chicago and Anaheim in the West race.
Los Angeles swept its season series with Calgary for just the second time in franchise history and the first time in 13 years. The Kings will get little chance to enjoy their achievements during their brutal March schedule featuring 17 games in 31 days: They hopped right on a plane after the game for a Pacific Division meeting with Phoenix.
"The schedule is hard, (so) you've got to find different ways to hang in there," Los Angeles coach Darryl Sutter said. "It means you're a good hockey team when you do that. We've found different ways to win games, and that's what you have to do. The schedule does win and lose games for teams."
Mikael Backlund ruined Quick's shutout bid with 5:22 to play for last-place Calgary, which has lost six straight on the road.
Joey MacDonald stopped 19 shots for the Flames, who got outscored 13-3 while losing all three games of their Southern California road trip, including a 4-0 blanking by Anaheim last week. Los Angeles routed Calgary 6-2 on Saturday, chasing Miikka Kiprusoff in the process.
"I think we just got outcompeted and outplayed," captain Jarome Iginla said. "The toll is that we just dropped three games on the trip, and we've fallen way back. But there's no excuses as far as scheduling or whatever. We had a chance to come in here and pretty much catch the Kings if we could have pulled these two games out, but it goes the opposite way."
After Saturday's loss by Calgary and Sunday's wins by Colorado, Columbus and Edmonton, the Flames began the week in 15th place in the West. The Flames realize they're running out of time to turn around their season, too.
"When you lose a couple of games in a row, your confidence gets down a little bit, and you're not ready for the next shift, and all of a sudden it's 2-0," Calgary coach Bob Hartley said. "You have to fight through that."
Brown swiftly put the Kings ahead in the rematch by sneaking behind Jay Bouwmeester and tucking home a sharp cross-ice pass from Slava Voynov for his seventh goal of the season. Moving the puck swiftly and easily, Los Angeles doubled its lead four minutes later when Jake Muzzin found Stoll in the slot for a shot that dislodged the water bottle from the top of MacDonald's net.
Muzzin, a rookie defenseman, had assists on both first-period goals, giving him 10 points this season -- the same number as Drew Doughty, Los Angeles' $56-million former Norris Trophy finalist and playoff hero. Muzzin also has five goals -- five more than Doughty, and tops among NHL rookie defensemen -- and a plus-11 rating in his breakout season.
After a scoreless second period, the Kings killed off a 27-second two-man disadvantage early in the third. Calgary kept dominating play, and Backlund finally capitalized when he undressed defenseman Alec Martinez and beat Quick low for his fourth goal of the season.
The Kings didn't even need a goal from Jeff Carter to wrap up their eighth home victory in nine games. The power forward had scored 13 of his 17 goals in his past 13 games, putting him in a second-place tie in the Richard Trophy race.
Kings C Tyler Toffoli was a healthy scratch, delaying his NHL debut. The high-scoring 20-year-old prospect was recalled Sunday from the AHL. ... Calgary D Cory Sarich, a healthy scratch in nine consecutive games, returned to the lineup in place of Derek Smith. Sarich hadn't played since Feb. 18. Flames LW Curtis Glencross missed his second straight game with an upper-body injury. ... Welterweight Ruslan Provodnikov attended the game, sporting a Kings jersey and cheering for Voynov, his fellow Russian. The Freddie Roach-trained boxer will take on unbeaten WBO champion Timothy Bradley in nearby Carson, Calif., on Saturday night.