Kim shot 8-under-par 62 Saturday for a one-stroke edge over PGA Tour rookie Scott Stallings after the third round on the Old White TPC course.
Kim's low round of the year left him at 10-under with a chance to advance to next week's Bridgestone Invitational with a win. He hasn't missed Firestone since his rookie year in 2007.
A third place-or-better finish would put him in position to earn a spot in the PGA Championship in two weeks in Atlanta heading into the FedEx Cup playoffs.
"I haven't had this much fun playing golf in a long time," Kim said.
Stallings shot 66 to move into second place at 9-under. Gary Woodland (67) and second round co-leader Webb Simpson (69) were two strokes behind Kim.
Kim's last victory came a year ago at the Shell Houston Open before he underwent thumb surgery and took three months off. He's had an up-and-down year, with eight missed cuts and two top 10s in 21 events.
Kim tied for fifth at the British Open earlier this month after making it as an alternate. But last week he was disqualified from the Canadian Open after signing for a score other than an 11-over 81 in the second round.
Kim credited a talk he had after the disqualification with his mother, whom he termed a "great golf psychologist."
"It was just about having fun, relaxing and enjoying the position I'm in because I'm very fortunate to be playing golf for a living," he said. "Sometimes you forget about that. I was pretty upset about my 81 and she noticed somebody in the gallery who was less fortunate. We talked about that and I came out here ready to play some golf and have a good time."
That's a stark contrast to the first six months of the year, in which Kim said he didn't want to be on the golf course because he wasn't sure where his shots would end up.
"People may think I'm exaggerating, but that's how tough this game got for me," Kim said. "Going back to the basics is really what helped my game. Because without that, I would still be struggling."
Kim made eight birdies, tying his total from the first two rounds combined. All of his birdies Saturday came from inside 10 feet. His 113-yard wedge to within a foot of the pin at the par-4 14th gave him the outright lead.
"I was just hitting smart golf shots," he said. "I was starting to think my way around the course instead of just get up to a tee and the fairways are 40 yards wide and the rough is not that penal and just try to hit it as hard as I can. That's not how you play golf."
Stallings had missed the cut in seven of 13 previous events since a third-place finish in the Transitions Championship.
Starting the day two strokes out of the lead, Stallings made four birdies. He missed a 34-footer for eagle at the par-5 17th that would have tied him with Kim, then missed a 13-footer at No. 18.
Stallings has gone 42 consecutive holes without a bogey.