Kunitz boosted the Penguins into a 2-2 tie with 3 minutes remaining in the third period, collecting the puck behind the net and burying it on a wrap-around move.
He struck again in the fourth round of the shootout, faking out Kings goalie Jonathan Quick with a feint to the right, then moving back to the left and sliding the puck underneath him.
Anze Kopitar and Simon Gagne found the net for the Kings, who fell to 1-4-1 in their last six games.
Quick finished with 31 saves.
Swim Week Miami Beach 2014 [PHOTOS]