Kim's free-kick was deflected off the wall and into the net after Hassan Maatouk's 12th minute strike had put the unfancied hosts ahead in Beirut.
Korea lead the table with 11 points from six games ahead of Uzbekistan on goal difference. Iran are third with 10 after their 1-0 victory over Qatar (7) in Doha earlier on Tuesday.
Lebanon remain bottom with five points and, like Qatar, have now played seven matches and have only one remaining.
The top two from the group qualify directly for next year's finals in Brazil, while the third-placed team will still be in with a chance of joining them via the playoffs.
Maatouk raised Lebanon's hopes of pulling off an upset win over South Korea when he slotted Mohamad Haidar's cross into the bottom left-hand corner of the Korean goal.
The stunned Koreans went on the attack but Lee Chung Yong hit the post after combining well with Lee Dong Gook.
The visitors mounted several raids but Lebanese goalkeeper Abbas Hassan thwarted them time and again to preserve the hosts' lead at half-time.
After the break Korea's forwards spurned a hatful of chances.
In the 72nd minute, Kim Keehee headed Kim Chi Woo's cross against the post and seven minutes later Lee Dong Gook failed to slot home from close range after Hassan denied Kwak Taehwi.
Deep into stoppage time Korea found a fortunate equaliser when Kim's left-foot free-kick was deflected into the net.