South Korea through after draw
Argentina's 2-0 win over Greece in the other Group B match had put Nigeria's destiny in their own hands but the Super Eagles spurned a string of chances and it is the South Koreans who will now meet Uruguay in Port Elizabeth on June 26.
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With hosts South Africa and Cameroon already out, and Ivory Coast and Algeria likely to join them, only Ghana now have a realistic chance of keeping Africa in the tournament.
South Korea, semi-finalists in Asia's first World Cup as co-hosts in 2002, had goals from Lee Jung-soo and Park Chu-young either side of half time to thank for reaching the last 16 for the first time on foreign soil in their eighth World Cup.
"It's the first time we are reaching the second round away from home," said South Korea coach Huh Jung-moo. "That was our goal. I'm very proud of my players. I feel that my players have played to their full potential."
Nigeria were aiming to be the first team to lose their first two World Cup matches and still get through to the knockout stage and Kalu Uche gave them the perfect start after 12 minutes.
After defensive errors let the South Koreans wrest the lead away from them, Yakubu Aiyegbeni restored parity from the penalty spot in the 69th minute.
The striker's fine spot kick was only part redemption for a howling miss in front of an open goal minutes before, however, and although none of the later Nigerian chances were as clear cut, a pattern was set.
With the news coming through from Polokwane that Argentina had taken the lead, the Nigerian bench waved their players forward but substitute strikers Victor Obinna and Obafemi Martins were unable to find the target.
"For me it was a good game, but all the same we're not happy," said Nigeria captain Kanu. "We did well, we created the chances but if you don't score goals you don't win and that's what happened."
South Korea, spurred on by Man of the Match Park Ji-sung, will take credit for a skillful and gritty performance that prevented them from being overwhelmed by the power of the West Africans.
It was a powerful run down the right from Chidi Odiah that produced the opening goal as the defender brushed off two Koreans to deliver a cross that Uche diverted into the net after getting in front of his marker.
South Korea struck back in the 38th minute when Ki Sung-yong swung a free-kick across the box to find Lee Jung-soo alone at the far post and he scrambled the ball into the net with a combination of head and foot.
The Nigerians' task became even harder when the Red Devils took the lead four minutes after the break from another of a series of free-kicks the West Africans conceded around the penalty area.
Park Chu-young stepped up and curled the ball around the wall and past the despairing dive of badly-positioned goalkeeper Vincent Enyeama.
With most of the crowd cheering them on, the Super Eagles continued to drive forward but the cheers turned to gasps and groans when an unmarked Yakubu missed an open goal from four yards out.
He recovered to convert the penalty after Kim Nam-il had upended Chinedu Obasi in the area but it was a blunder that ultimately summed up Nigeria's night.
"What is the problem for Africa in general?" asked Nigeria coach Lars Lagerback. "It's really small margins when you are playing at this level."