The outstanding Hirving Lozano smashed home the Mexican winner in the 35th minute at Moscow's Luzhniki Stadium, leaving Manuel Neuer clutching at thin air on his return to the German goal after a nine-month injury absence.
Toni Kroos crashed a shot against the crossbar for Germany but they were never able to get back into the match as they slid to their first defeat in their opening game of a World Cup since 1982.
"I don't know if it's the biggest win in Mexico's history but doubtless it is one of the biggest for sure," said 22-year-old Lozano.
Lozano's winner made the earth move in Mexico City, where seismologists detected a minor tremor possibly caused by "widespread jumping during the goal."
Germany coach Joachim Löw did not mince his words about his side's performance, saying his team had played "very badly" in the first half of the Group F tie.
"We weren't able to impose our usual way of playing, our attacking and passing was not effective," he said.
"It goes without saying that the next match will be decisive for us, we have to win it," Löw added ahead of his team's next game against Sweden next Saturday.
If Germany finish as group runners-up, they could face Brazil in a clash of World Cup titans in the next round -- a perfect chance for the Brazilians to avenge the humiliating 7-1 defeat to the Germans on home soil in 2014.
Brazil, and their star Neymar, made their bow in Russia in Rostov-on-Don but gutsy Switzerland battled back to cancel out a Philippe Coutinho strike midway through the first half of the Group E tie.
The Barcelona man found the top corner with a stunning curled effort in the 20th minute but Steven Zuber headed an equaliser from a corner shortly after half time and the five-time champions could not make their superior quality count.
Coach Tite blamed first night nerves.
"I'm not happy with this result. Our finishing wasn't good. We had 20 chances, but too many shots were off target. We should have made their keeper work harder than that.
"I put it down to stress, first match nerves, that's true for me too," the Brazil boss said.
German disarray
Germany had breezed through qualifying, scoring 43 goals and conceding just four.
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