Trailing 4-3 after Jonathan Toews scored for the Blackhawks 3:51 into the final frame, the Kings charged back.
Toffoli scored the equalizer on a long flip shot that floated past a screened Corey Crawford at 8:06 and Brown put in the game-winner with just 1:27 remaining when he scored on the rebound of his own first shot.
The Blackhawks, meanwhile, dropped a second straight despite Crawford's 31 saves.
Michael Frolik scored twice and added an assist for Chicago.
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