Twitter is now in meltdown after the exited the group stage for the first time since 1938.
Germany, before Wednesday, had not missed the knockout rounds since 1950 when the side was banned from the World Cup.
Victory for Sweden against Mexico would secure their place in the knockout stage. Alvarez also scored Mexico's fourth own goal in World Cup history, also a World Cup record, as it takes them past both Bulgaria and Spain.
The Germans, who won the last World Cup four years ago, were beaten 2-0 in Kazan after two injury-time goals.
Both Sweden and Mexico qualified for the last 16 with Germany crashing out in stunning fashion after losing to South Korea.
There were a plethora of permutations in Group F ahead of kickoff but Germany started in Kazan knowing that a victory by two goals would be enough to progress, regardless of what happened in Mexico vs. Sweden in Yekaterinburg. But they came out with an uninspired effort against South Korea, and Germany's failure came in especially gut-wrenching fashion. This is now a record for most penalties converted at a World Cup, surpassing the 17 conversions in 1998. The 1994 was a thriller, finishing 3-2 to Germany, but the 2002 match was all the more significant considering the fact that it was a semi final.
The presence of veterans like Gianluigi Buffon and Fabio Cannavaro and that of Marcello Lippi on the bench could not prevent Italy from being humbled in the group stage as they failed to win any of their matches.