The Swedes won the group on Wednesday after beating Mexico 3-0, but the central Americans also went through. A long punt upfield saw Tottenham forward Son Heung-min chase a clearance to fire into an empty net and Korea hung on for a famous win that will be a consolation for their own elimination.
Meanwhile, Sweden finished top of Group F on goal difference after the win against Mexico, with both teams on six points.
Mexico take on the mighty Brazilians in Samara on Monday, hoping to progress to the quarter-finals for the first time since 1986.
Germany have been eliminated from a World Cup in the first round for the first time since the Second World War, as the holders are knocked out in the group stage for the fourth time this century. "It was the best thing, we just passed to the next round, and the World Cup champion is out". It was a stunning result, both for the team that had come to Russian Federation as the world's No. 1 and for South Korea, which wasn't listed in the top 50 when this tournament began.
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Germany were caught out at the back as they threw men forward in search for a late victor, with Kim Young-Gwon flicking home inside the box two minutes into injury time. "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.
"We believed until the end even with the 0-1 (deficit) we tried to turn it but we could not score", said Hummels, after Germany became the tournament's third champions in succession to go out at the group stage.
Despite being flagged offside initially, the goal was eventually given after VAR got involved, with the final touch before the goal actually coming off a German player.
"At this tournament we didn't deserve to win again or move to the round of 16".
Prior to the World Cup, Jo was the least experienced of the three custodians on the national team with five caps.
He said: "Until quite recently, we have probably been the most consistent, in terms of performance, team in the past 10, 12 years".
Germany lost on Wednesday despite dominating in possession - 69 percent to 31 percent - and leading South Korea in shots on goal.