Solheim Cup hopefuls Emilee Klein (67) and Nancy Scranton (68) joined Shani Waugh (67) and Laura Diaz (67), who is in second place on the American Solheim Cup points list, at minus 12.
Kim had only 104 yards to the flag at the par-4 17th and chose an 8-iron. She knocked it short of the hole and after two bounces and a little roll, the ball fell in for an eagle and gave her a share of the lead at 13-under-par.
'It was dead on line, one or two hops, then right in,' said Kim's caddie Chris Birdseye. 'It kind of rolled in.'
The eagle capped a brilliant back nine for Kim, who earlier fell down the leaderboard with three front-nine bogeys. At the 10th, Kim hit a pitching wedge inside a foot for the tap-in birdie. She made it back-to-back birdies at 11 when she hit a 7-wood to five feet.
Kim duplicated her approach from 11 at the 13th, where once again a 7-wood shot stopped five feet from the hole to set up a birdie to reach 10-under-par. The South Korean took advantage of the par-5 15th when she reached the green in two and two-putted from 20 feet for birdie.
'On the front nine, I wasn't hitting good,' said Kim, a two-time winner on tour this season. 'Then at the turn, my caddie said just be patient. So I just tried to be patient. Then on number 10, tap-in putt. So I was feeling very good.'
While Kim was torching the back nine, Meunier-Lebouc was hanging on as her driver let her down. She held sole possession of the lead after a pair of birdies at 10 and 12 but it went downhill after that.
At the par-4 14th, Meunier-Lebouc drove right, nearly against a tree. Her only play was a punch 6-iron because of her low back swing and she advanced the ball toward the hole, but remained in the rough. She played her second 12 feet from the hole but missed the par save to drop to 13-under-par.
Meunier-Lebouc's driver let her down at the par-5 15th as she found the rough on the right side. She could not reach the putting surface in two but her third shot from 47 yards failed to get up a ridge in front of the pin. Meunier-Lebouc rapped her birdie try eight feet past the hole but converted the clutch save to stay at minus 13.
The dangerous par-3 16th tested Meunier-Lebouc as she avoided water right of the hole but found a greenside bunker left of the putting surface. She blasted out to eight feet and holed that par putt to keep pace at 13-under-par.
She parred the remaining two holes to stay even with playing partner Kim and is now in position for her first LPGA Tour title.
'I had a lot of tension and I think I was into the reality today,' said Meunier-Lebouc, a member of the 2000 European Solheim Cup team. 'Maybe a little bit too much. I was not able to get out of the game, get my head into the clouds like you say. It took a lot of energy today to play golf.
'I'm still there. That's why I think I kept trying. You know, somewhere inside, I told myself to stay trying hard to stay in there.'
Akiko Fukushima, who played in Saturday's final group with Kim and Meunier-Lebouc, was tied for the lead on the 18th hole but stumbled with a double-bogey. She carded a 1-under 71 and is tied for seventh with Angela Stanford (68), Pat Hurst (68) and Cristie Kerr (69) at 11-under-par 205.
Full-field scores from the State Farm Classic