Germany would have progressed with a win at the Kazan Arena but barely looked capable of scoring against the Koreans, let alone going on to successfully defend the title they won in Brazil four years ago.
Stoppage-time goals from South Korea’s Kim Young-gwon and Son Heung-min finished off Joachim Loew's sorry Germany side, who finished bottom of the group on three points.
The four-time winners, who had not been eliminated in a World Cup first round since 1938, were a shadow of their once dominant selves, managing only two goals in their three group games.
The Germans needed to beat Korea by two clear goals in their final group F match at Kazan stadium to advance to the last 16.
But Joachim Loew's men wasted a series of chances in a tense match that saw a pale version of the world champions become the fourth holders of the title this century to be sent packing at the first hurdle.
Video assistance in final minutes
Germany's team of superstars could only look on in shock in the final minutes of the match as US referee Mark Geiger called for the video assistant referee to intervene after the unmarked Kim had bundled his shot past Germany goalkeeper Manuel Neuer from a corner early in stoppage time.
The goal was awarded because Toni Kroos' touch had played him onside, and minutes later Germany were 2-0 down after Neuer ran up the pitch in a desperate attempt to get a goal.
A long punt upfield saw Tottenham forward Son chase a clearance to fire into an empty net.
Germany coach Joachim Loew caused a surprise by leaving midfield attacking stalwart Thomas Mueller on the bench for the first time since 2012 after his underwhelming displays against Mexico and Sweden.
But by the end of a frustrating opening half, Loew was left desperately studying his options.
Germany suffered the first of several scares after South Korea won a free kick on the quarter hour when Sami Khedira's boot connected with the head of Jung Wooyoung.
From 30 yards out, it should have been fodder for World Cup-winning goalkeeper Manuel Neuer, but after fumbling Jung's dipping drive Neuer scrambled desperately to clear as Son raced to pounce.
Germany spurned a series of chances soon afterwards.
Sweden beats Mexico, powers into last 16
With Sweden winning 3-0 against Mexico in the other Group F game, and it being goalless in Kazan, Germany knew they had to score in a frantic finish.
The Swedes went through to the knockout rounds as the unlikely winners of Group F, taking the beaten Mexicans with them.
Second-half goals from defenders Ludwig Augustinsson and Andreas Granqvist, from the penalty spot, plus a comical own goal were reward for a physical display from Sweden, who only made it to Russia by beating Italy in the play-offs.
They and Mexico, who were ragged throughout, will next play whichever two teams emerge out of Brazil, Switzerland and Serbia in Group E, which concludes later on Wednesday.
Mexico came into the game at the Yekaterinburg Arena in the driving seat in a group where all four teams, including South Korea, could qualify, but they appeared the more nervous.
It took them less than 30 seconds to make their mark on Sweden, Jesus Gallardo earning a yellow card for clattering into Ola Toivonen almost straight from kick-off.
Goalkeeper Guillermo Ochoa handled outside the box and then flapped at the resulting free-kick. On 12 minutes Marcus Berg clipped wide from close range with a bicycle kick.
On the quarter-hour mark, Mexico, who had the overwhelming support inside the stadium, should have taken the lead when Carlos Vela found himself in space on the edge of the box.
His bending left-footer shaved the post, catapulting a few sombreros off the heads of Mexico fans as they expectantly sprang to their feet.
They were up again on 30 minutes when referee Nestor Pitana of Argentina took a look at a video replay when the ball hit Mexico striker Javier Hernandez on the arm in the box.
After lingering at the pitch-side monitor, then going back for a second glance, Pitana ruled it no penalty -- the Mexicans celebrated as if they had scored a goal.
The Swedish players and coach Janne Andersson were furious, and understandably -- Hernandez appeared to move his arm towards the ball.
Sweden, with their greater physicality, were on top, but Mexico were dangerous on the break.
At the interval, with the game also goalless in Kazan, Mexico and Germany were going through.
Sweden badly needed a goal and five minutes after half-time they deservedly got it, defender Augustinsson popping up from left-back to volley in.
A 74th-minute own goal
There was more drama on the hour, as Hector Moreno brought down Berg in the box and skipper Granqvist held his nerve in front of the massed ranks of Mexicans to bury his penalty.
Plastic beer cups rained down, before Mexico defender Edson Alvarez compounded a miserable evening with a 74th-minute own goal when he miskicked past Ochoa.
That left Mexico in a perilous position, as a late German winner would have sent the Central Americans crashing out, but two injury-time South Korean goals in Kazan ensured Juan Carlos Osorio's men edged through as runners-up.
Mexico will need to pick themselves up quickly if they are to go beyond the last 16 for the first time since 1986 and end a run of six consecutive second-round defeats.
(FRANCE 24 with AFP and REUTERS)