Germany is out of the World Cup, the fourth defending champion in the last five tournaments to be eliminated in the group stage.
While the Germans were clumsy in front of goal, Kim Young-gwon and Son Heung-min scored late while their teammates defended superbly with last-minute tackles and hard collective work.
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.
German soccer fans had their hopes of a fifth World Cup title dashed on Wednesday after watching their team crash out of the tournament in the opening round for the first time in 80 years.
Loew's side began their campaign with a 1-0 defeat to Mexico before rekindling their bid with a last-gasp 2-1 win over Sweden.
In Russia, Germany were nowhere near the compact unit which conceded just four goals in seven games at the 2014 World Cup. "Even when it was 0-1, I think we kept trying to turn it all around".
When the going got tough on this occasion, he and Germany failed on the world stage, any sense of euphoria embarrassingly vanishing. "We need to draw the right conclusions".More news: Suarez Says Rivalry With Ronaldo Different When Playing for Uruguay, Barcelona
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Mexican fans in Russian Federation for the World Cup also expressed their gratitude to one South Korean they found outside the stadium in Ekaterinburg following the defeat to Sweden.
"Since we won, everything went as planned", South Korea Coach Shin Tae-yong said. I couldn't imagine that we would lose to South Korea.
Meanwhile in Yekaterinburg, Sweden dominated Mexico 3-0 to move on to the World Cup knockout round. "We lost but we're in the next round", Alcocer said, "So, we're very happy".
South Korea controversially claimed their first goal in stoppage time after yet another VAR blow-up saw a potential off-side call land in favour of the underdogs. "We looked at their strategies for the past four days". But this is the third straight World Cup in which the previous champion has been knocked out before the end rounds.
Loew had changed his line-up to mix youth with experience, calling back Hummels, Sami Khedira and Mesut Ozil while also fielding Niklas Suele and new Bayern signing Leon Goretzka.
"Germany are the defending champions and No. 1 in the Federation Internationale de Football Association ranking, so I thought about what mistakes Germany might make, because they probably felt they would be able to beat us - that's what everybody thought", South Korea manager Shin Tae-yong told reporters. Loew said he had not yet reflected on the future.