Starting the final round in a tie for 11th, Kim shot a four-under 68 to finish 14 under par, three shots behind Yuri Yoshida of Japan, who won by a stroke.
Kim's surge lifted her two places to 56th in the season-long points race, with the top 60 to qualify for next month's rich and prestigious Tour Championship in the US.
It came after she climbed from 62nd to 58th with an equal-13th finish in Shanghai last week.
The news was not so good for compatriot Karis Davidson.
She improved to reach a tie for 15th on Sunday at a wet Pine Beach Golf Links with a three-under 69, having begun the day equal 19th.
But she still dropped four spots in the points race, clinging to a Tour Championship berth in 59th position.
Australia's Hannah Green is already assured of making the field in Naples, Florida, from November 19-22, sitting in 12th spot.
Compatriot Cassie Porter also looks safe in 47th, despite struggling in the BMW to finish 68th after a closing 73.
But triple major-winning superstar Minjee Lee is languishing in 78th spot in the points race with two events left before the $US11 million ($A16 million) season finale.
Lee carded a three-over 75 to finish well down the leaderboard in equal 74th, at three over.
Kim found her touch through the middle of her final round.
After cancelling a birdie two on the third with a five on the fourth, she put together five birdies in eight holes to the 14th, to look a chance for the lead at 15 under.
But a bogey four at the 15th soured her bid, and she could manage only three pars to finish off, ending in a four-way tie for sixth. The 25-year-old took 30 putts in her round, hitting 16 greens in regulation.
Davidson began well with a birdie four at the second, but stumbled with bogey fives at the fifth and seventh. She steadied to revive her tournament - and her hopes for Florida - with four birdies in her bogey-free last 11 holes.
Yoshida played superbly to notch her first career victory in dramatic circumstances.
Four shots off the pace on Saturday night, she turned in five-under par after an unblemished front nine of three birdies and an eagle.
The 26-year-old conceded her second back-nine bogey on the last to card a four-under 68 and finish on 17 under.
Fortunately for Yoshida, Haeran Ryu - who blew a four-shot overnight lead - also bogeyed the last to leave her Japanese rival one shot ahead.
Ryu (73) shared second with fellow South Korean Hye-Jin Choi (69).
With AP.
