Richards scored in the sixth round on a wrist shot from the slot that got past Ray Emery to the glove-side.
Kings goaltender Jonathan Quick stopped Blackhawks forward Viktor Stalberg's backhand deke in the shootout. Quick had blocked Stalberg's penalty shot in the third period.
Kane's goal tied the score 7:36 into the third period.
Quick had 35 saves for the Kings, who ended a two-game losing streak.
Emery notched 27 saves for Chicago.
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