Kim Young-gwon scored the first goal in the third minute of injury time, a goal that sent the Koreans cheering in Kazan and the Mexicans delirious in Yekaterinburg.
GERMANY has been sensationally booted out of the World Cup before the knockout stage for the first time since 1938. South Korea's Son Heung-Min added another goal a few minutes later in one of the most shocking results in soccer history, officially eliminating defending champion Germany.
Sweden beat Mexico 3-0 in the other Group F game, allowing both those sides to advance to the second round.
The defending champions went into the final game of the group stage knowing a win against South Korea would likely see them through to the last-16 if the other result went their way.
Germany lost the opening game 0-1 to Mexico, and dramatically beat Sweden 2-1 in stoppage time for the second game.
The curse of the World Cup winners continues.
"We're very disappointed, but for such a match - they really have to go home", he said.
Germany suffered the first of several scares after South Korea won a free kick on the quarter hour when Sami Khedira's boot connected with the head of Jung Wooyoung.
The shot was initially ruled offside, but the Video Assistant Referee system confirmed it hit the legs of Germany's Toni Kroos before finding the South Korean's foot.
We are sorry for not playing like world champions, and as painful as it is, we deserve to be out.
The Germans had denied Guus Hiddink's South Korea a place in the 2002 final with a 1-0 win in Seoul after the co-hosts had ridden a wave of national footballing fervour to defeat Poland, Portugal, Italy and Spain on the way to the last four.
Germany's best chance before going behind had fallen to Mats Hummels late on, but the defender wasted it, paving the way for South Korea's late show.
Fellow supporter Denis, who travelled nearly 3,000km (1,864 miles) from his home in Stuttgart to watch Germany take on South Korea in Kazan, was equally resigned.
South Korea will be one of the favourites to win the tournament, which begins in early January and runs until early February - which is a blow for Tottenham Hotspur.