Ludwig Augustinsson volleyed a left-footed shot past goalkeeper Guillermo Ochoa from close range five minutes into the second half, and captain Andreas Granqvist converted on a penalty to help Sweden take control Wednesday and win Group F. They were still in position to advance despite trailing Sweden, but they were waiting - some with tears in their eyes - for Germany to do the inevitable and ruin their chances of moving on.
Germany finished bottom of Group F after a 2-0 defeat against South Korea.
"Like you, were are not just dreamers, but work hard to make those dreams come true".
"We still have not qualified but who would have said we would have six points by now?" asked Hernandez, a former Manchester United forward who always appears happiest wearing the green of his country. "We beat the world champions, that's not so easy", said Luis Padilla, 29, a cafe owner in Mexico City, voicing cautious optimism that the team would continue bringing happiness to the fans back home.
Loew had changed his line-up to mix youth with experience, calling back Hummels, Sami Khedira and Mesut Ozil while also fielding Niklas Suele and new Bayern signing Leon Goretzka. Suele made his first World Cup appearance as a replacement for Jerome Boateng.
Italy have historically been slow starters in World Cups.
The Germans continued at the same pedestrian pace after halftime and Ozil had another poor display, with many of his passes uncompleted. After 10-man Germany beat Sweden 2-1, thanks to superb free kick goal by Toni Kroos in the 95th minute, South Korea were given an extra life.
Germany ended up last in a group it expected to win.
But the Germans never really got going this time, losing their opening match to Mexico 1-0.
Korea coach Shin Tae-yong said he had mixed feelings after the win over Germany as it was not enough to take them through.
On Monday at 9pm, Brazil will face Mexico, with the match to be shown on Amarin TV.
Four-time winners Germany, 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.
"It's too soon for me to answer, it will take a few hours to see things clearly, the disappointment is very deep in me", the 58-year said when asked if he would resign.