The 25-year-old South Korean closed with a one-over 73 to finish at 8-under-par 208, one stroke ahead of fellow countrywoman Hee-Won Han.
Kim held a three-shot lead over Han with two holes to play but knocked her tee shot with a 5-iron off a bank and into the water guarding the 148-yard 17th. Since rules officials determined her ball didn't cross the line of the hazard on the bank, Kim had to go back to the tee to hit her third instead of getting to play the shot from the drop area.
She landed her ball 12 feet from the hole the next time around but two-putted for a double-bogey five, cutting her advantage to one.
At the par-4 18th, Kim split the fairway with her drive then hit a 7-iron approach right of the green. Her ball wound up at the base of the grandstand and, after getting a free drop from the temporary obstruction, played a skillful chip to three feet.
Meanwhile, Kim's playing partner Han hit the green with her second shot but was left with a 45-foot putt to tie the lead. Han missed her birdie attempt, and Kim sank her short par putt for the win and the $150,000 first prize.
The victory was Kim's fifth in four years on the LPGA Tour and her second in the last three weeks. She came from behind to beat Kelly Robbins at last month's Giant Eagle LPGA Classic, which was also in Ohio.
Kim, the 1999 LPGA Rookie of the Year, also has a pair of second-place finishes this season. She finished four shots behind Annika Sorenstam at the Evian Masters, then a week later surrendered a five-stroke lead in the final round to Karrie Webb in Rochester.
Next up for the diminutive Kim (the LPGA generously lists her at 5-foot-1) is the Women's British Open at Turnberry. Last year in the rain-plagued event at Sunningdale, Kim fired a 65 in the second round en route to a runner-up finish behind Se Ri Pak.
'I just hope the weather is good,' Kim said.
For Han, who carded a final-round 70 to finish at 7-under par, Sunday marked her second straight runner-up showing. She lost in a playoff to another Korean, Gloria Park, in last week's Sybase Big Apple Classic.
Danielle Ammaccapane shot 70 for third place at six-under 210. Lorie Kane, who won this title in 2000, turned in a 70 for a share of fourth with Michele Redman (71) at minus-five.
Rosie Jones (71) was next at 4-under par.
Rookie Candie Kung made a run at the top of the leaderboard with two birdies and an eagle through 12 holes Sunday. However, she dropped four shots on the final three holes for an even-par 72 and tied for seventh with Barb Mucha (69) and Betsy King (71) at minus-three.
Last year's winner, Wendy Ward, finished nine shots back at one-over par.