Hungary shocked Austria in the opening Group F game as they won 2-0 thanks to second-half goals from Adam Szalai and Zoltan Stieber.
Szalai fired home after a neat one-two and Zoltan Stieber rounded off a late breakaway with an outstanding chip to give the underdogs the points in the 138th meeting between the two sides.
Austria had been a fraction away from the fastest goal in European Championship history when David Alaba fired a 20-yard shot across goalkeeper Gabor Kiraly — the oldest player in European Championship history — after just 28 seconds but hit the post.
That was soon followed by an effort from Hungary's Laszlo Kleinheisler, who fired a 25-yarder straight at Austria keeper Robert Almer.
With 10 minutes gone, Austria had another chance when Marko Arnautovic played Alaba through, but his strike was stopped by Kiraly.
Laszlo Kleinheisler fired over for Hungary, who again unsuccessfully tried their luck from distance through Zoltan Gera.
Austria, who had defender Aleksandar Dragovic booked for a foul, wasted a promising free-kick position when Alaba smacked his strike into the wall.
Their frustration grew when Zlatko Junuzovic's bouncing attempt drew a fine one-handed stop from Kiraly.
Martin Harnik scuffed wide after an exchange of passes with Arnautovic before it was Hungary's turn to be frustrated when, just before the break, Balazs Dzsudzsak dragged past the post when well placed.
Right at the start of the second half, Attila Fiola had a shot saved by Almer — but after 63 minutes, Hungary made the breakthrough.
Szalai combined stylishly with Kleinheisler and slid the ball home from inside the area for his first goal in 41 matches.
As Austria's composure faded, they were reduced to 10 men when Aleksandar Dragovic received his second yellow card for a late challenge on Tamas Kadar.
And with Hungary growing in confidence, Adam Nagy fired over the top and Krisztian Nemeth saw a fierce strike flash narrowly wide of the far post.
Austria tried to ramp up the pressure in the closing minutes but were unable to seriously test Kiraly — and they were undone when Stieber raced through to provide the coolest of finishes over a helpless Almer.