Lewis stayed in contention for her 12th LPGA victory with a 67 that included six birdies in the first 11 holes, before she stalled down the stretch and allowed Kim to zoom to the front.
Kim bogeyed the 13th hole but stormed back immediately with a hat-trick of birdies.
She gained international prominence when she won the Evian Championship, an LPGA major, last year.
A victory here would set the 19-year-old up nicely for a tilt at a second major title at the ANA Inspiration in the California desert in two weeks.
Lewis was happy with the quality of her game, if not thrilled by her score.
"Today I felt like I played a lot better than I scored," she told Golf Channel.
"I had a bunch of putts right around the edge. I'm looking forward to tomorrow. I feel like I've put myself in contention a lot and should hopefully handle things pretty well tomorrow."
New Zealand's world number one Lydia Ko was within striking distance, four shots behind after a 69.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
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