Joachim Lowe's men were sluggish from the off, their pre-tournament form on display at the Luzhniki Stadium with Mexico racking up chances but unable to find the finishing touch.
Carlos Vela and Javier Hernandez were both guilty of making the wrong decision when in good positions until Hirving Lozano finallyl broke the deadlock.
The young striker skipped onto Chicharito's pass and into the area, wrong-footed Mesut Ozil and beat Manuel Neuer from 14 yards for his eighth goal for Mexico.
Germany, who have outscored opponents 20-2 in its past four World Cup openers, went into the break trailing but showed improvement after the break as Mexico retreated.
Julian Draxler, Timo Werner and the introduced Marco Reus were lively as Germany chased an equaliser but Mexico posed a significant threat on the counter and Chicharito twice found himself in a good position but fluffed his lines.
Rafael Marquez came on with 15 minutes to play, appearing in his fifth World Cup in his 17th finals game, and his country needed him with wave after wave of German attack.
Reus tried his luck on the angle with a volley before Kroos's first-time effort whistled the wrong side past the post. Mario Gomez was introduced with 10 minutes to play and had arguably Germany's best chance with a header six yards out but was unable to get his effort on target.
It was not to be for Germany as Mexico held on for a famous win.
