The regular time ended goalless as both sides failed to break the deadlock.
Seokhun Choi gave South Korea the lead with a header in the fifth minute of extra time.
The Flying Eagles were the dominant side in the encounter but they couldn’t find a way past the dogged South Koreans.
Kim Joonhong produced a fine save to deny Victor Ehuwa Eletu in the regulation time.
In the second half, Nigeria looked more adventurous with defender Daniel Bameyi striking from the edge of the box, only to see his effort stopped by the goalkeeper. In added time, Emmanuel Umeh’s dazzling run ended with a shot that was also smartly held by the Korean goal-tender.
Seokhun Choi headed in Lee Seungwon’s to give South Korea the lead and ultimately a place in the last four of the competition.
Umeh, with a great chance to equalize in the 109th minute, blazed over the bar, and in the final minute, struck the side of the net.
The Asians will now face Italy in the semifinals on Thursday.
The Flying Eagles will return to the country on Tuesday.