Spectators watched the match on a big TV screen in the central Zocalo square and after the game, they converged around the iconic Angel of Independence monument waving Mexico flags. Find out by following our live matchcast.
Low's side had 26 shots, the most by a side without scoring in a World Cup match since 2006 (Portugal v England, 29 shots in a 0-0 draw).
Hirving Lozano has wrong-footed Germany's Mesut Oezil and scored from about 14 yards out to give Mexico a 1-0 lead over the defending World Cup champions.
Germany's preparations for the tournament were plagued by poor results and controversy, and their problems were magnified in the Russian capital, leaving their proud record of never being eliminated in the group stage of a World Cup already in danger.
Germany will be looking to become the first country since Brazil in 1962 to successfully defend their World Cup crown.
"Our motto was play with the love of winning and not the fear of losing", Osorio said after the match, Reuters news agency reports. The Mexico coach has kept quiet about his strategies and in warm-up matches revealed very little on how he plans to stop the Germans.
"We need the greed, the fire - it's part of what makes things go off with a bang sometimes in training and on the playing pitch".
Osorio had to endure vociferous criticism after a 7-0 defeat by Chile at the Copa Centenario in 2016 and again after their performances at the Confederations Cup past year, including a semifinal defeat to Germany. Germany will now be under pressure when they face Sweden next in their second group tie.
Mexico is not the clear favorite in Group F but they will definitely try to take avenge of the 4-1 defeat against Germany on their last encounter.
One desperate last attack had Neuer come up for a corner, but a towering header from the veteran Marquez and subsequent claim from Ochoa allowed Mexico to close out an unforgettable triumph.