Austria, who had a new lease of life after dismal defeats by Belgium and Turkey earlier this year, did more than enough to end a run of five successive defeats against their neighbours.
But all they had to show for their efforts was an Arne Friedrich own goal early in the second half of an absorbing Euro 2012 Group A qualifier that was balanced on a kife edge.
There was a certain inevitability about the outcome as Gomez took advantage of two defensive lapses, the second in the 90th minute, to chalk up a sixth successive group win.
With 18 points from six games, Germany have almost clinched a place in Poland and Ukraine but Austria stay fourth with seven points, four adrift of Belgium, who have played a game more, and three behind Turkey after they drew 1-1 in Brussels.
The Austrians need to finish second to have any chance of qualifying through the play-offs but with only four matches left, including one in Germany, that looks beyond them.
"We made lots of mistakes, we were a little bit lucky to win the game today," Friedrich told ARD television. "It was an important win although we did play as well as we could."
Coach Joachim Low said Germany, missing key midfielder Bastian Schweinsteiger and talismanic striker Miroslav Klose through injury, made too many mistakes.
"We were rather lucky," he agreed.
AUSTRIA DECLINE
Austria and Germany used to be share one of Europe's fiercest rivalries but recent matches have become embarrassingly one-sided following the former's decline.
Austria have not beaten Germany in a competitive match since their 3-2 win at the 1978 World Cup in Argentina and their last victory in a friendly was 25 years ago. Recent results have included 3-0, 3-1, 6-2, and 5-1 wins for the Germans.
When the two sides last met, at Euro 2008 which Austria co-hosted with Switzerland, Michael Ballack's goal gave Germany a 1-0 win which ended Austria's hopes on the only occasion they have ever played at the European championship.
Gomez was among eight survivors from that game - four on each side - while Austria's starting line-up included five German-based players.
A lively start saw Martin Harnik head narrowly wide in the fourth minute for Austria before the visitors replied by creating a flurry of chances.
The best opportunity saw Gomez flick the ball wide of the post after a quick-passing move sliced open the Austria defence before Lukas Podolski rifled a left-foot shot against the crossbar from 25 metres.
BETTER SIDE
Gomez headed into the arms of Christian Graetzei from five metres but after that Austria were the better side.
Erwin Hoffer had the hosts' best first-half chance, poking the ball wide after a superb drag-back, but Germany went ahead with their next attack when Gomez scored from close range as the Austrians failed to clear a
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