"(Brown) played fantastic for us tonight," said Kings defenseman Drew Doughty, who also had a goal and an assist. "That's why he's our captain, he's our leader. When he's playing his best, he leads the way and we all follow."
The Kings started this weeklong trip in Detroit with a 3-2 victory Saturday. Next up is a game at Columbus on Thursday, before they finish with back-to-back games against Boston and New Jersey.
The Kings have 63 points, two behind fifth-place Phoenix in the Western Conference.
Jonas Gustavsson made 28 saves and Niklas Hagman scored twice for the Maple leafs, who lost their fourth straight.
"It is frustrating to have opportunities you can't finish off," Maple Leafs coach Ron Wilson said. "That wasn't what was frustrating tonight. It was losing battles, and losing races to pucks. And that's the frustrating part."
It was Gustavsson's third straight start for the Leafs. The 25-year-old signed a one-year deal in July, and was 9-11-8 heading into Tuesday night.
"I know there are about 30 games left and my contract is coming up after the season, so I know I have to play good to show that I want to stay here," Gustavsson said before the game. "I know it's up to me to show that I want to be here, and I want to be a goalie the team can count on."
The Leafs had been on the road for five games, returning home with four losses following an uninspiring trip through Florida.
"We need the points," Leafs wing Jamal Mayers said. "And we have to find a way to get some wins together."
Los Angeles took a 1-0 lead on a power-play goal from Doughty after Toronto defenseman Ian White was sent to the box for tripping.
Nikolai Kulemin tied it for the Leafs four minutes later.
Jack Johnson, Jarret Stoll and Ryan Smyth all beat Gustavsson in the second.
"I thought we kept a pretty good game plan," Brown said. "No one really overextended themselves trying to do too much, which can happen in a building like this."
Brown's most notable assist came on Stoll's goal.
The Kings' captain, also named an alternate captain for the U.S. Olympic team earlier this month, stripped the puck from Leafs forward Wayne Primeau along the side boards and scooted toward the net, dishing off to his wide-open teammate.
NOTES: As part of a pre-game tribute to better times, retired fan favorites Dave (Tiger) Williams, Lanny McDonald and Norm Ullman were invited to conduct the ceremonial opening face-off. Toronto players had worn throwback uniforms from the 1970s in their pre-game warm-up ... The Kings are set to send five players to the Vancouver Olympics next month: Brown (U.S) Jack Johnson (U.S.), Quick (U.S.), Doughty (Canada) and Michal Handzus (Slovakia).