But Kim missed and instead settled for a closing 10-under 62 that tied the Wildfire Golf Club course record.
Kim finished at 27-under 261, while world number one Lydia Ko (65) of New Zealand claimed second place on 22-under.
Karen Stupples, of England, holds the LPGA record for lowest numerical score, 22-under 258, set at the Dell Urich Golf Course in Tucson, Arizona, in 2004.
"It's a dream come true," Kim told Golf Channel. "Today's score, 10-under, is my best score ever, ever. So I didn't know that after the last putt, but after I check the scorecard, I asked my caddy, 'Did I shoot 10-under?’ He said, ‘Yeah,’ Oh, my God. That's amazing."
Kim began the final round one shot behind fellow South Korean Ji Eun-hee. Kim, however, left the field behind with five birdies in her opening eight holes. She added an eagle at the 11th and three more birdies in her final six holes for her fourth LPGA Tour win.
Ko finished strongly with four straight birdies on her back nine, beginning at the 13th, but it was too little, too late.
"There are not many times when you shoot seven-under on the last day and only a few groups behind (the leader) and still finish five shots behind,” Ko said.
(Editing by Andrew Both)
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