Uruguay made it to the second round as surprise winners of Group A after holding France to a goalless draw, beating hosts South Africa 3-0, and closing with a 1-0 win over Mexico, Ajax striker Luis Suarez getting the all important goal.
Uruguay won the inaugural World Cup on home soil in 1930 and followed up in 1950.
They crashed out on their last appearance in the competition in 2002 when co-hosts South Korea made it into the semi-finals.
A last four place is again the target coach Huh Jung-Moo has set for his Asian giants in South Africa.
"We have achieved our first objective of reaching the round of 16," Huh, an accomplished changgi (Korean chess) player, said.
"After that, anybody can guess what our next objective might be, but I know that the players will immediately set a higher target.”
"They won't be satisfied now with just having progressed. They will want to get to the semi finals."
South Korea have punched above their weight in South Africa to finish runners-up in Group B.
They opened in style with a 2-0 win over former European champions Greece, on their first visit to Port Elizabeth's Nelson Mandela Bay stadium.
A 4-1 rout by Argentina followed but they put that reverse behind them when holding Nigeria to a 2-2 draw in Durban on Tuesday.
After securing their last 16 ticket Huh observed: "It's the first time we reached the second round at a World Cup abroad. I'm very proud and very happy," Huh said.
"I feel my players played to their full potential and were not intimidated."
South Korea captain and Manchester United winger Ji-Sung Park, who scored in the win over Greece, added: "It's a first for us to qualify away from home and we're very pleased to have done it here in South Africa.
"All the players know how tough it is to do, but I'm very proud of the players at having done so."
Uruguay coach Oscar Tabarez has warned South Korea that his side are improving.
"I don't think we have achieved all we want yet," Tabarez said.
"As a coach it is very satisfying to see how the group has evolved. This is an excellent group, there is cohesion and friendship among the players and they are really dedicated to the job they are doing."
Share
