The result means both teams depart the tournament while Sweden win Group F and are joined by Mexico in the last 16.
Germany finished bottom on goal difference.
Sweden, who beat Mexico 3-0, have topped the group, with Mexico coming second.
The two South Korean’s goals were scored on added time.
South Korea are also packing their bags but they go home having knocked out the defending champions.
Kim Young-gwon scored South Korea’s first goal on 92 minutes. Toni Kroos got the last touch so Kim Young-gwon was onside when the ball landed to him six yards out and he smashed it into the roof of the net.
On 96th minute, Son Heung-min made it 2-0 for South Korea.
Manuel Neuer is just outside the South Korean box, Ju Se-jong lumped the ball 80 yards down the pitch and Son Heung-min was able to tap the ball into an empty net.
Earlier, Kim Young-gwon had turned a shot home from six yards but the flag went up and it was disqualified.
Germany had struggled at the World Cup, losing 1-o to Mexico in their opening game and managed to beat Sweden 2-1 in the second game before being embarrassed and dumped out by South Korea.
Germany’s shock exit from the World Cup is the first time Die Mannschaft have failed to make it out of the group stage since 1938, per Opta:
2 – This is only the second time that Germany have been eliminated from the First Round at the World Cup having last done so in 1938. Shock. #GER #KOR #KORGER #WorldCup pic.twitter.com/jIZWOlxeEw— OptaJoe (@OptaJoe) June 27, 2018
The defending champions qualified in style but struggled in their World Cup warm-up games, and they could not turn their form around when they arrived in Russia.
A defeat to Mexico set the tone for their campaign, and although they managed a dramatic last-gasp win over Sweden, their loss to South Korea proved costly.
Manager Joachim Low must take the blame for their early exit. His decision to omit Leroy Sane from his squad will return to haunt him particularly as the team struggled in attack.
Low chose Julian Brandt over Sane, but the Bayer Leverkusen man barely featured. Freelance writer Archie Rhind-Tutt highlighted his lack of game time:
— Archie Rhind-Tutt (@archiert1) June 27, 2018
The Germany boss made some big decisions in the three games as he dropped Mesut Ozil for the win over Sweden, while Thomas Muller was axed for the defeat to South Korea.
The changes did little to improve the team who looked complacent, disjointed and lacking in ideas. Germany would have expected to win the group but finished bottom and did not deserve a place in the knockout stages.