Then six minutes into stoppage time, with Germany goalkeeper Manuel Neuer in possession in the opponents' half, Ju Se-jong gained control of the ball, launched it forward and Son Heung-min tapped into an empty net to score the second.
The goal was initially ruled out for offside, but the decision was overturned following a video review.
However, neither team seriously threatened to score and the only unsafe chance was from a swerving Koo Jacheol free-kick that caused Manuel Neuer some difficulty, but the goalkeeper managed to block it and then flick the ball away just in time before Son Heungmin could get to the rebound.
Germany's victory over Sweden was their first at the World Cup when conceding first since 1998, a 2-1 win over Mexico. After being humbled by Mexico in their opening game, they managed to snatch a win against a very ordinary Sweden side with a last-gasp Toni Kroos free-kick.
It was, though, a bittersweet success for the Koreans, who exited the tournament as well, despite becoming the first Asian side to defeat the Germans at a World Cup, as Sweden beat Mexico and both teams advanced.
Despite enduring what has thus far been a frustrating World Cup, Timo Werner will now hope to end his wait for a first goal at a major tournament here against what is the weakest opponents Germany have faced so far in Russian Federation.
Shin, heavily criticised back home for the 1-0 defeat to Sweden and the 2-1 loss to Mexico in their previous outings in Russian Federation, said the win over Germany was all due to his meticulous preparation.
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To watch Germany vs South Korea online, all you need to do is fire up BBC iPlayer, which doesn't cost a penny if you've got a valid UK TV license.
Reigning world champions Germany were sent crashing out of the World Cup after suffering a stunning 2-0 defeat to South Korea.
On a warm and sunny afternoon at Kazan Arena, some 42,000 flabbergasted fans witnessed the fall of a titanic team who had made the semi-finals or beyond in every World Cup since 2002. "It's an open goal for Son and the Germans have got what they deserve". "Even when it was 0-1, I think we kept trying to turn it all around". In addition, Julian Draxler had a disappointing game against the Swedes and was replaced just after the restart, meaning we could potentially expect Mario Gomez to start upfront with Timo Werner being shifted into a wider role.
With Sweden comfortably beating Mexico in the other game, Joachim Low's side knew that they needed to score to stay in the competition.
But it was Kim Young-gwon who broke the deadlock in added time when he found himself alone in front of goal after a corner and he poked the ball home from close range.
Quite the opposite, in fact: it shows Joachim Low in sunglasses, interrupting his morning jog in the Black Sea resort of Sochi to lean on a street lantern, posing for an agency photographer.
"We have to be masters of our own destiny", said Germany head coach Loew.