Maple Leafs goalie James Reimer stopped Anze Kopitar in the tiebreaker but Brown then unleashed a shot in the third round that rang off the post, beating Reimer on the glove side for the game winner.
Darryl Sutter is expected to be introduced as the Kings' new head coach Tuesday or Wednesday.
John-Michael Liles and Matt Frattin scored and Reimer finished with 40 saves for the Maple Leafs, who fell to 2-5-3 in their last 10 home games.
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