Kim recovered from an early bogey to pick up seven shots, including three from his final four holes, to join Americans Brandon Wu and Ryan Moore at the top of the leaderboard on nine-under par.
Moore and Wu recorded just one bogey each en route to second round scores of 66 and 67 respectively.
The leaders sit one shot ahead of Russell Henley, John Huh and Sungjae Im, with the top nine players separated by just two strokes.
England's Tyrell Hatton carded a three-under 67 to lead the British contingent at five under, with Scotland's Martin Laird a shot further back.
"I mean just, I mean, all I did was laugh, I didn't really take it - it's just one bad hole," said Joohyung Kim after his bad start.
"I told myself, you know what, I've got plenty of holes to bring it back if I just play well on my next 35 holes, and that's exactly what I did.
"I played better than I thought I was going to, so it's a bonus.
"Yeah, I am just definitely happy to finish the round today and just kind of laid back knowing I've got the weekend to play."