In one of the great World Cup upsets, Kim Young-gwon and Son Heung-min both scored in added time to condemn footballing superpower Germany to their first opening-round exit in 80 years.
The win over Germany on Wednesday came after defeats to Mexico and Sweden, and they finished above the four-time World Cup winners on goal difference in Group F.
"We didn't make it to the round of 16... but we sent the world number one packing," said a headline in Seoul's major Dong-A daily.
"We are so proud of you," the newspaper said on its front page.
Germany went into the game knowing that a win by two clear goals would have seen them into the last 16. But instead it was Sweden and Mexico who advanced after the Scandinavians romped to a 3-0 win in the group's other match.
The Taeguk Warriors, semi-finalists in 2002, brought the defending champions "down with them", Yonhap news agency said, adding that Germany "unceremoniously bowed out of the tournament".
Korea Republic's social media was flooded by tens of thousands of messages from fans expressing joy and astonishment over a victory that had seemed utterly implausible before the match.
"This is far more shocking than our advance to the semi-final at the 2002 World Cup," one commenter said.
"Who cares we won't make it to the round of 16? We defeated Germany, the world number one!" added another.
"It was an honourable exit."
Prime Minister Lee Nak-yeon joined them, tweeting on Thursday: "Reality beat our imagination today" and praising the Korean footballers.