"I really wanted another win, especially this week, because the last two weeks I play really bad," Kim said.
Thompson, a stroke behind Kim entering the day, closed birdie-eagle for a 66.
"She played some amazing golf," Thompson said. "I didn't have my best ball-striking day, but 5 under, finished well. She played amazing. It's very well deserved."
Six shots ahead of Thompson (photo below) after the birdie run, Kim played the final seven holes in even par, offsetting a birdie on 15 with a bogey on 16. Kim broke the event mark of 263 set by In-Kyung Kim in 2017.
She's focused on winning her first major title, with The Evian Championship and Women's British Open coming up.
"I haven't had a win a major tournament yet," Kim said. "I think I try too much when I play the major tournament. I just play the same as regular tournament, even major. ... Just let it go. Let it happen."
Stacy Lewis was third at 16 under after a 66. She was born in nearby Toledo.
"It was a lot of fun," Lewis said. "More putts have gone in this week than in the years past. It was nice to give my family something to cheer for."
U.S. Women's Open champion Jeongeun Lee6 had a 69 to finish fourth at 14 under.
Jennifer Kupcho tied for fifth at 11 under after a 71, playing alongside Lewis.
"Getting to play with Stacy — and Lexi yesterday — seeing how their ball-striking is and how good their iron game is, definitely something to work on and definitely can learn and did learn from their games," Kupcho said.
The former Wake Forest star won the inaugural Augusta National Women's Amateur in April.
Linnea Strom (65), Tiffany Joh (67), Caroline Masson (68) and Pavarisa Yoktuan (69) also were 11 under.
Kupcho earned a spot in the Women's British Open along with Joh, Strom, Yoktuan and Mariajo Uribe.