Javier Hernandez triggered a lightning break 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. "It's great to start on the right foot when you are playing the world champions".
Most expected Germany to win Group F at a canter with the other three sides left to battle it out for second place. They qualified from the group stage but exited after a 3-2 loss to Austria in the next phase.
Germany hit back, Toni Kroos rattling the crossbar with a 25-yard free-kick that needed the fingertips of a scrambling Ochoa to keep it out, but Mexico barely clung on to their advantage.
At 39, Rafael Marquez became just the 3rd player to feature at 5 World Cups as he was brought for the final 15 minutes to fortify Mexico's defense.
Lozano's goal at the Luzhniki Stadium earned Mexico just the second win over Germany in history, as Loew's side paid the price for a dismal first half.
Germany didn't go quietly though, giving Low something to build on.
It means Mexico celebrated its goal so hard that it created its own natural disaster.
"We had a couple of shots on goal but somehow it seemed jinxed, the ball wouldn't go in". The Germans were being dominated in midfield and every time the ball broke in the centre, the Mexicans swarmed in numbers.
Coach Juan Carlos Osorio's bold approach - often leaving three attackers up the pitch even when defending set-pieces - paid off, as celebrating fans in Mexico City caused a minor natural disaster.
Mexico goal scorer Hirving Lozano, whose strike caused a small tremor on the Richter scale in Mexico City, ostensibly from fans jumping in celebration, was named man of the match.
Kimmich is a risk-taking defender who likes to venture forward but will have to be careful against Mexico as Lozano is a very unsafe player and who when given space will exploit it to Mexico's advantage.
Germany had the more possession but it was Mexico who were more creative.
Mexico is scheduled to train at its complex outside of Moscow on Monday morning in preparation for its match against Korea on June 23 in Rostov.
Some Twitter commentators and fans were quick to draw parallels between the Mexican team's long odds ahead of the Germany match and the big lead in surveys enjoyed by leftist presidential candidate Andres Manuel Lopez Obrador, or AMLO.