The Kings will enter the postseason as the sixth seed in the Western Conference and will draw Vancouver in the first round.
As the eighth seed, the Avalanche will play San Jose in the opening series.
Los Angeles tied the game late in the third when Jarret Stoll redirected a shot past Craig Anderson.
Ryan Stoa scored the lone goal for Colorado.
Kings goalie Erik Ersberg had 31 saves filling in for Jonathan Quick.
Brown's game-winner came when he poked in a shot off a rebound. It was his 24th goal of the season.
The Kings nearly won the game with 30 seconds remaining in regulation, only to have Anderson stop Alexander Frolov's point-blank shot with his right pad at the last moment.
Prior to Stoll's goal, the Kings' best scoring chance came courtesy of a misplayed puck by Anderson in the opening period. The Avalanche goalie tried to clear it from behind the net, only to have Anze Kopitar poke it away and nearly score.
Other than that, Anderson was solid all afternoon — all season really. Anderson set franchise records for starts, minutes played, shots faced and saves.
Stoa scored his second goal of the season midway through the first period, slipping a puck through the pads of Ersberg.
It would be the only mistake Ersberg would make all day.
The Avalanche held out Matt Duchene (torso) and Peter Mueller (head), two of their biggest offensive threats in recent weeks.
Duchene hurt his torso in a center-ice collision against Edmonton on Wednesday. He played in the first period of Friday's loss to Chicago, but left when the injury flared up again. The rookie of the year candidate was taken to the hospital as a precaution and later discharged. Duchene entered the day leading all NHL rookies in goals (24) and points (55).
Mueller has missed the last four games after taking a hit along the boards against San Jose. Mueller has accumulated 20 points since being acquired from Phoenix at the trade deadline.
NOTES: Kings C Michal Handzus was given the game off to rest up for the playoffs. ... Avalanche F Milan Hejduk picked up his 21st assist of the season on Stoa's goal. ... Kings D Drew Doughty has 43 assists this season after setting up Brown's game-winner.