Coming off horrible seasons in the German first and second divisions, Adam Szalai and Zoltan Stieber made the difference for the Hungarians. They caught an uninspired Austria completely off guard, winning 2-0.
Featuring a host of Bundesliga and Premier League players, Austria were the clear favorites over Hungary, who were playing in their first major tournament in 30 years, as Group F got underway in Bordeaux.
The Austrians almost scored the quickest goal of the tournament, when Bayern Munich's David Alaba, playing in midfield, fired a rocket from 25 meters after only 29 seconds. But he was denied by the post.
But Hungary quickly found their feet and even enjoyed a slight advantage in possession, albeit without creating any clear chances. It took more than 30 minutes for Austria to threaten again. The oldest player at the event, 40-year-old keeper Gabor Kiraly got down quickly to block a shot by Bremen's Zlatko Junuzovic.
Marko Arnautovic pushed his way through to the touchline in minute 41, but Stuttgart's Martin Harnik made a mess of his cross. Hungary then got their first look on goal just before the half, but the angle was too tight for Balazs Dzsudzsak. The first half ended scoreless.
The break did nothing to boost the Austrians. Instead the Hungarians seemed to gain confidence in the second half and took a not-undeserved lead on the hour mark. Adam Szalai played a neat one-two with Laszlo Kleinheisler, and the much-criticized Hoffenheim and Hanover striker put the ball in the net.
Things went from bad to worse for Austria when defender Aleksander Dragovic headed for the showers after a second yellow card deep in Hungary's half. Austria had enough trouble creating chances with 11 men - down to ten, they couldn't trouble Hungary at all.
The momentum had shifted entirely. The Hungarians had a clear advantage in shots on goal, and three minutes from time, Zoltan Stieber made it 2-0 with a chipped goal on the counter-attack. It was lights out for Austria - Hungary were ultimately good value for their victory.
Hungary will face Iceland on Sunday in Marseille, while the Austrians have what could be a must-win clash against group favorites Portugal in Paris.