The Koreans remain on course to qualify for an eighth successive World Cup finals after they grabbed the point they needed in their final Group B game against their 91st ranked opponents.
Kuwait hit the post before Lee Dong-gook opened the scoring for South Korea in the 64th minute. Lee Keun-ho then doubled the advantage six minutes later in new coach Choi Kang-hee's first competitive game in charge.
Choi was appointed after South Korea were shocked 2-1 by Lebanon in November which put their place in the 10-team fourth round in doubt.
However, victory on Wednesday meant they qualified for the March 9 draw as group winners.
The win also meant that Lebanon reached the fourth round as group runners-up despite a 4-2 loss away to United Arab Emirates on Wednesday.
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