After going behind in the 12th minute, South Korea equalised when Lee Chung-soo latched onto a free-kick from just outside the penalty area and then took the lead after the break when Park Chu-young curled another freekick around Nigeria's wall.
Many players at the World Cup in South Africa have criticised the new Jabulani ball, likening it to a beachball, and the tournament has been littered with free-kicks being blasted high over the bar.
Spain striker Fernando Torres was the latest player to blame the ball on Tuesday after he squandered several scoring opportunities in their 2-0 win over Honduras a day earlier.
"We trained quite a lot for the free-kick and from that position, and Park Chu-young was the one for the freekick," South Korea coach Huh Jung-moo told a news conference.
"Compared to other balls, if you kick it too hard then 80 to 90 percent of the time it seems to go up in the air, too high. So we trained so that it would be kicked lightly, without hitting it too hard.
"I think we adapted well to the ball."
Nigeria gave away 22 free-kicks in the final Group B match in Durban's Moses Mabhida stadium, many for ill-timed challenges within striking distance of goal.
South Korea now play Uruguay in the second round in Port Elizabeth on June 26 and are shooting for the the semi-finals, which they reached in 2002 on home soil when they co-hosted the World Cup with Japan.
Huh said he thought the group stage of the World Cup was tougher than the knockout matches as they come down to which side controls the flow of the game on the day.
"In the case of Uruguay, they are very strong on the counter-attack so we are going to have to be fully prepared," he said. "Among the South American teams, Uruguay is very strong and they are tough players."
South Korea showed grit and determination against Nigeria, coming from behind and battling to seize control of the midfield after a strong start from the West Africans.
"We have shown that Asian football has come of age," said midfielder Ki Sung-yong. "We have created history and shown the world that we are one of the best teams in Asia."
