Bennett, 24, ended a difficult third day on Saturday on a high with a birdie on the par-five 18th hole.
It meant she signed for a one-over 73 which lifted her to outright third spot at six-under 211.
Bennett will play in the final group at 13th Beach on Sunday with leader Madoka Kimura (nine under) and fellow Japanese player Shina Kanazawa (seven under), who had led after both of the opening two rounds.
"I hung in there well today," said Bennett, who will play full-time on the Ladies European Tour in 2025.
"I lost it a bit in the middle of the round so it was good to have the birdie on the last.
"I tried to keep telling myself that everyone is in the same boat, to try and hit good shots.
"I got a couple of shots wrong with the wind and it was just a bit messy today so hopefully I can tidy it up a bit."
Bennett said the real battle was to keep her focus in tricky conditions at the links layout.
"I feel bad for my caddy because I take it out on her all the time," she said.
"It's hard to stay focused, but all it takes is one good shot or one good putt and you're back, you get that confidence back."
Bennett has yet to win a four-round tournament as a professional, so if she salutes on Sunday it would be the biggest victory of her career.
Kimura replaced Kanazawa atop the leaderboard on Saturday after shooting the low-round of the day - a four-under 68.
Kanazawa had led after both of the opening two rounds but found the going tougher on Saturday as she carded a two-over 74.
Australian-based LPGA Tour regular Jenny Shin (72) was in outright fourth at five under.
Another South Korean, pre-event favourite and former world No.1 Jiyai Shin, shot a four-over 75 and is seemingly out of contention at two over.
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