In a meeting of the top two teams in the Pacific Division, Los Angeles inched within three points of the front-running Sharks.
Evgeni Nabokov kept the Kings off the scoreboard for the last 31:30 of regulation, but he surrendered Brown's seventh goal of the season in the extra period. Nabokov made 23 saves in the loss.
Erik Ersberg, starting for the first time in almost a month, allowed four goals on 34 shots to get his second victory of the season.
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