The Koreans are top of Group A after their victory over Lebanon, ranked 143rd in the world by FIFA and appearing in the fourth stage of World Cup qualifying in Asia for the first time.
The Lebanese had stunned the Koreans 2-1 in Beirut in the previous round, but there was no repeat on Tuesday when the visitors struggled to get the ball, let alone create chances.
The two-time Asian champions opened the scoring in the 30th minute when Kim's long-range effort found its way past visiting goalkeeper Ziad El Samad.
The Koreans, who thumped Qatar 4-1 in their opening fourth round match in Doha on Friday, played with little urgency and had to wait until early in the second half to extend their lead.
From a Lebanese corner, the Koreans broke away and Kim was left in acres of space to run through and slot home left-footed in the 47th minute.
Substitute Koo Ja-cheol wrapped up the scoring a minute before the final whistle. Hussein Dakik attempted to bring the ball out of Lebanon's penalty area but Koo dispossessed the midfielder before unleashing a powerful drive.
The home side are aiming to reach their eighth consecutive World Cup finals. Lebanon remain bottom of the five-team pool, on one point, after their home draw with Uzbekistan on Friday and an opening loss to Qatar.