Nam Tae-hee's first-half header was the only goal as Korea claimed a second successive win at the continental championships in Australia.
In the 30th minute Korea created the first genuine chance, with Kim Min-woo releasing Lee Keun-ho down the middle, but Hameed Youssef saved the striker's shot.
Cha set-up South Korea's opening goal in the 36th minute with a cross towards Nam, who headered the ball powerfully through Youssef's hands.
Kuwait started the second half well with Ali Al Maqseed hitting the post.
The Middle Eastern side seemed to gain the upper hand and in the 60th minute Al Maqseed’s shot narrowly went over the bar.
Korea’s Lee Keun-ho almost scored a minute later, attempting to curl the ball into an empty net from a tight angle and with 15-minutes left he missed with a header.
In the end South Korea will be happy with the win from a tightly contested encounter.
Korea have 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.