But Mexico were creating by far the better opportunities and coach Juan Carlos Osorio was soon awarded for his flawless tactical plan. After wasting a handful of first-half chances while living dangerously in their own half, Hirving Lozano's 35th-minute strike on the break proved just reward.
After Sami Khedira lost possession, Javier Hernandez triggered a lightning counter before finding a charging Lozano, who cut inside a covering Ozil and lashed low inside Neuer's near post to spark deafening roars from the sizeable Mexico support. Only two teams prior, Italy in 1938 and Brazil in 1962 had managed to do it. "Teams develop and change, players finish their careers and you must bring in new players which makes it the most hard achievement".
"We will not suffer that fate", German coach Joachim Low said through a translator.
Marco Reus, who missed the last two tournaments through injury, came off the bench against Mexico and Julian Draxler, one of Germany's better players on Sunday, has become a favourite of the German manager. The current Mexican team is a blend of experience and youth.
"But today we deserved to win for what we showed, ran and gave".
Brazil also suffered a 0-0 draw against Scotland but beating Zaire ensured they progressed to the second group stage, from which they had to settle for a spot in the third place pay-off.
Mexico's aggressive approach unsettled the entire German team, particularly their central defensive pair - Jerome Boateng and Mats Hummels - and their number 10.
Osorio's strategy against the four-time champions was speed on the wings with the 22-year-old Lozano, his fastest player, and Miguel Layun.
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To further compound their problems, goalkeeper Sergio Romero and midfielder Manuel Lanzini both fell victim to late injuries. But the Icelanders revel in their underdog status and showed at Euro 2016 they will not be cowed on the big stage.
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He said cancellation of the drills "is really a bad idea ... and (Trump) betrayed our people". He has the power to remove most State Department workers without oversight.
Meanwhile, Germany, the only team to have made it made it to the second round of every World Cup since 1954, needs at least a tie against Sweden on Saturday to keep that streak from ending. Low's dropping of Sane from his 23-man Finals squad has caused consternation, and this was a game in which Germany could have done with his pace and guile.
But it was not to be.
Mexico, the perennial underachievers, who so often arrive at big tournaments on a wave of optimism only to crash out at the first hurdle, began the game with a bang.
However, qualification is no certainty now as Sweden and South Korea are no pushovers. But they put in a disastrous performance in their opening match, losing 5-1 to Netherlands in a game that will be remembered for a stunning flying header scored by Robin van Persie.
But their reputation is not what it was.
Hummels felt Germany did not heed the warning of their final warm-up friendly against Saudi Arabia that ended in a tight 2-1 win, their only success in seven matches since the end of the World Cup qualifying campaign a year ago.
"We are now under pressure. Yesterday we practiced defending with four midfielders and three players up front and that was how we nearly got the second goal today".