Michal Handzus and Kyle Quincey scored power-play goals and Erik Ersberg made 24 saves to help the Kings extend their winning streak to four games with a 3-2 victory against the Stars on Thursday night.
The teams met on Tuesday night in Los Angeles in a physical game that the Kings won 3-2 in a shootout. That game included a fight late in regulation between the captains, Brown and Dallas' Brenden Morrow.
Brown had checked Dallas' Mike Ribeiro into the boards while Ribeiro was vulnerable after taking a shot, opening a gash over Ribeiro's eye that required 10 stitches.
Morrow quickly began pummeling Brown with punches, and Brown swung back. Morrow earned an instigator penalty and a game misconduct while Brown received a major for boarding and a game misconduct.
A physical night was anticipated in the second leg of the home-and-home games, but there was nothing even close to a fight.
"I thought it would be a little more physical," Brown said. "But it's always physical when we play Dallas."
The Kings were 1-7 in Texas during the previous two seasons, but they led all the way in their first visit to Dallas this season.
"On the road in general it's tough," Brown said. "But we played pretty well tonight. We came in here and grinded it out."
Jarret Stoll added his sixth goal of the season for the young Kings, who simply played harder than the veteran Stars.
"Our work ethic wasn't there and until we realize it, we'll keep going down in the standings," Stars defenseman Stephane Robidas said. "They're a young team without a lot of experience, but all their guys work hard. I think we've hit bottom. If you're not willing to put your work boots on, it's going to be hard to win in this league."
Brad Richards and Ribeiro had power-play goals for Dallas. The slumping Stars lost for the fifth time in their past six games to fall into last place in the Pacific Division.
"We seem to be a flat team, with a lead or when we're down a goal," Morrow said. "We're getting a good shift followed by a bad one. Then we get pressed again and a goal will go in against us. We're a foot short. We're throwing the puck at the net but we're not relentless enough to follow up."
Dallas coach Dave Tippett said he's seeing too much individual play from his team.
"We have to continue to pound away," Tippett said. "We have to take the individual stuff out and put the team first. If we get to the point where they don't want to do it, we'll move them out of the lineup."
The Kings opened the scoring at 9:53 of the first period when Handzus' power-play deflection got past goalie Marty Turco. Dallas' Sean Avery had been sent to the penalty box for tripping four seconds earlier.
Stoll's deflection at 13:11 of the opening period made it 2-0.
Dallas pulled with 2-1 with 21 seconds left in the first period during a 5-on-3 when Richards' one-timer from the high slot went in off Kings defenseman Sean O'Donnell's stick.
Los Angeles stretched its advantage to 3-1 when Quincey's one-timer from the blue line got past a screened Turco at 3:24 of the second period.
Dallas cut it to 3-2 at 14:43 of the second period on Ribeiro's deflection.
LW Fabian Brunnstrom, the object of an offseason free-agent recruiting battle that involved more than 20 NHL teams, was a healthy scratch for the Stars. Brunnstrom is minus-7 in 13 games. ... Stoll played in his 300th game.