The 38-year-old from Sydney followed up her 68 and 67 with a two-under 69 to be sitting nine under and joint-ninth, seven strokes behind leader Chanettee Wannasaen.
Kemp's bogey-free round included birdies at the eighth and 15th holes.
Grace Kim (73) is the only other Aussie playing over the weekend and is one under the card.
A celebration-worthy birdie putt by — LPGA (@LPGA) @kempgolf �Tune in to catch the Round 3 action on @Peacock! pic.twitter.com/28ROq8lFWlJuly 20, 2024
Thailand's Wannasaen fired a five-under-par 66 on Saturday to continue her blistering start.
She drained six birdies, including one at the 18th to cap her round, extending her Friday lead from a single stroke to three.
Wannasaen, who previously won the Portland Classic in 2023, has collected 17 birdies against just three bogeys over the first 54 holes.
"Yeah, I didn't expect," Wannasaen said.
"But I really play well this week."
She got off to a steady start with birdies at the second and ninth holes while posting pars the rest of the front nine. She got hot with three straight birdies at Nos. 12-14 before a bogey at 16 and her final birdie at 18.
"I think I'm going to like don't think about the result, because I don't want to get stress for tomorrow," Wannasaen added.
"So like just stay in present time. Don't think about the future."
One-time LPGA Tour winner Chanettee Wannasaen remains the player to catch in Ohio. (AP PHOTO)
Wannasaen's closest competitor is South Korea's Haeran Ryu, who sits at 13 under after firing a six-under 65.
Defending tournament champion Linn Grant (70) of Sweden fell an additional four shots off the pace, leaving her in a tie for third place with Taiwan's Ssu-Chia Cheng (66) and Xiyu Lin of China (70).
"I just stay patient out there," Cheng said.
"I didn't really have the best start like today or even just like the past two days. I just kind of stayed patient out there and just one shot at a time."
A stroke behind those three is another trio who are tied for sixth place at 10 under. That group includes Lucy Li (67), South Korea's Hyo Joon Jang (64) and China's Mary Liu (70).
Jang's round tied American Malia Nam's for the best of the day.
With AAP.
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