Michael Ballack's spectacular second-half strike handed Germany a last eight tie against Portugal at the expense of Austria who exited Euro 2008.
Germany should have scored early in the match but Mario Gomez somehow missed from two yards.
Austria's best chance fell to Andreas Ivanschitz whose shot was blocked.
"We were a little bit nervous in front of the goal and maybe that's why Gomez missed," said the Chelsea midfielder.
"We might have missed that chance but we fought to the end."
Ballack added: "It was a good free-kick. I hit the ball very well and it was important to score early in the second half."