However, South Korea came back roaring, with two daring Cho Gyu-sung headers three minutes apart to equalize the seesaw match.
Kudus grabbed the winner in the 68th minute when he was left unmarked in the penalty area and headed past a diving Kim Seung-gyu.
Things got heated after referee Anthony Taylor blew the final whistle. In the closing moments of extra time, a long range shot by a Korean player deflected off a Ghanaian player and went past the Ghanaian goal post.
The Korean players were expecting a corner kick but the referee blew the final whistle instead.