Nam Tae-hee's first-half header decided the contest in driving rain in Canberra, as South Korea claimed a second successive win at the continental championships in Australia.
The victory took South Korea to six points and a goal difference of plus two, ahead of Australia's (three, plus three) clash with Oman (zero, minus one), while Kuwait (zero, minus four) are eliminated after two straight losses.
South Korea made seven changes from their 1-0 win over Oman, with a virus reportedly to blame for coach Uli Stielike's decision to name just seven players on his bench.
Having confirmed just before kick-off that midfielder Lee Chung-yong would miss the rest of the tournament due to a fractured right leg, South Korea also started without Son Heung-min, Koo Ja-cheol and Kim Chang-soo in the squad.
Lee Keun-ho led the line for South Korea as part of a brand new front four with Lee Myeong-ju, Kim Min-woo and Nam, while Cha Du-ri and Kim Young-gwon were promoted in defence, and Kim Seung-gyu started in goal.
Kuwait made four changes of their own from their 4-1 loss to Australia on the opening day of the Asian Cup.
But the alterations looked to have made little difference early in the match, as South Korea dominated possession without creating too much in front of goal, while Kuwait were forced to rely on counter-attacks.
It took South Korea until the half-hour mark to create the first genuine chance, with Kim Min-woo releasing Lee Keun-ho down the middle, but Hameed Youssef saved the striker's chip.
The chance seemed to inspire Stielike's side, however, with Cha becoming more involved from right-back.
Cha set up South Korea's opening goal in the 36th minute, whipping a cross towards Nam, who put enough power into his header to ensure the ball squeezed through Youssef's hands.
With elimination looming, Kuwait started the second half at full pace with Ali Al Maqseed hitting the post, while a free-kick fell to Fahad Al Hajeri in the six-yard box, although the defender failed to control the ball.
Kuwait's energetic pressing saw the Middle Eastern nation gain the upper hand with Al Maqseed curling a shot just over the bar in the 60th minute.
But the attacking intent of Nabil Maaloul's men left gaps in defence and Lee Keun-ho almost scored a minute later, attempting to curl the ball into an empty net from a tight angle, while the striker missed a header with 15 minutes left.
The game became stretched in the final minutes as Kuwait desperately tried to keep their qualification hopes alive, but Stielike's side held on.
