Mexico fans were hoping for a shocking upset - and the South Koreans delivered that with two goals in stoppage time for a 2-0 victory.
Son has emerged as a real leader for the South Koreans.
Paulinho and Thiago Silva scored a goal each for Brazil and the five-time champions will next face Mexico in the round of 16 on Monday in Samara.
Joachim Low's side head home after a stunning failure, having been unable to break down the South Koreans and after a shock 1-0 loss to Mexico in their opening group match.
"We were rightly eliminated from the tournament".
"It is a very bitter evening for us and for all German football fans".
Yet they scarcely looked capable of scoring, let alone going on to claim another trophy.
Their first-round exit in 1938 was in the days when the tournament had a straight knockout format; in the eighty years of first round group stages since that era Germany have never been eliminated before the knockout rounds. They yelled continuously as the celebration grew inside the stadium.
Half chances came and went, prior to Hummels' miss off his shoulder in the 87th minute.
"It is a really, really bitter evening for us", admitted Hummels, who squandered a late chance when he headed over.
"Today it was not easy but, yes, no team could get through easily".
But it was South Korea that made the first serious threat at the goal when the Asian side were awarded a free kick opportunity in the 18th minute. "We advanced to second phase, and thanks to Korea!" said Mexico City resident Edmundo Robert, who was at the game with his son and father-in-law.
He later told a news conference: "Where we go from here, we have to think about it calmly, it will take me some hours to come to terms with it".
Hogging 70 per cent of possession and launching 26 shots at goal, Germany pushed forward in numbers but found no way through the Korean stonewall.
Four minutes later, Son Heung-Min doubled the score on a counter attack, putting the ball in the wide open goal. VAR confirmed there was nothing wrong with Kim's precise finish after the linesperson initially flagged for offside.
Thomas Müller tried to keep everyone calm, informing his teammates that they still had six minutes to work with, but Germany lost it and panicked. After losing the opener and barely tumbling over the line in the second, the Germans went into the match against South Korea clutching three hard-earned points, the affluence of goals starkly missing in action.
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