The Cerezo Osaka left-footer grabbed his first two goals in 14 senior internationals, and Koo Ja-Cheol added a late third as the 2002 FIFA World Cup semi-finalists made it two wins in a row to start the final qualifying phase.
The Taeguk Warriors beat Qatar 4-1 in Doha last week, while Lebanon fell to Qatar and drew against Uzbekistan before making the long trip east. Tuesday's win also avenged the Koreans 2-1 reverse in Beirut last November, which cost former coach Cho Kwang-Rae his job.
It was a slow start to the evening in Goyang, west of Seoul, as both teams looked fatigued. With the visitors seemingly content to sit back, Korea Republic were unable to penetrate until Kim opened the scoring with a rocket from just inside the box in the 29th minute.
The left-footed midfielder took a sharp cross from Lee Keun-Ho and put a thunderous strike past goalkeeper Ziad El-Samad off the bottom of the crossbar. Just after half-time, Kim was released near the centre after a botched Lebanese corner, and he drove in on El-Samad before chipping it over the advancing 'keeper.
The winger nearly picked up a hat-trick when he fired narrowly wide of the right post near the hour-mark. FC Augsburg's Koo then pounced on a defensive error to lash home the third goal on 89 minutes.
At the other end, South Korean goalkeeper Jung Sung-Ryong rarely tested but he pulled off a diving save to keep out a Mouhamad Chamass shot late in the game.
South Korea have played in every FIFA World Cup final since Mexico 1986. Lebanon, winless after three games in the ongoing round, are seeking their first World Cup berth.
The Taeguk Warriors are currently top of five-team Group A. The top two sides in both of the two groups qualify automatically for Brazil 2014, while the third-placed teams go into the play-offs.