"One must say we won this game through luck... The Austrians fought hard and ran well. We made a lot of mistakes," Germany coach Joachim Löw told journalists after the game.
"But only the result counts in a game like today," he said as Germany stayed on course to Euro 2012 qualification with their sixth win in as many games.
"There was a sensational atmosphere, it was a difficult game as expected," German striker Lukas Podolski added.
"Austria was a strong opponent especially in the second half, they put on a lot of pressure. In the end they would have deserved a point," he said.
Up until the 89th minute when Gomez hit the net a second time, Austria was set for a much-needed draw and a rare result against traditional rival Germany.
But despite the loss, Austria's performance raised some hopes about the team, after two defeats in their last two Euro 2012 qualifiers against Belgium and Turkey.
"When you see how they played, I think if they keep playing like that, they have a good future ahead," Podolski noted.
Austrian Captain Christian Fuchs added: "This is the performance we've been talking about. We need to have more confidence and today we didn't just react, we acted."
"I think we can all be proud of the team's performance," he added.
"Play-wise, it was OK. A lot of what we had planned to do succeeded," Austria coach Dietmar Constantini noted.
"At times, we were definitely on a par (with the Germans). To lose 2-1 at the very end, that is very bitter."
Austria had the first chance after barely four minutes when Stuttgart striker Martin Harnik shot the ball just wide.
Germany retaliated shortly thereafter with a first effort by Gomez that trundled past Austrian goalkeeper Christian Gratzei, followed by Lukas Podolski, who hit the crossbar and another scramble in front of the Austrian goal, providing the hosts with more than a few scares in the first 10 minutes of play.
Gratzei stopped another shot three minutes later. Halfway through the first half, the hosts roused themselves with a long shot by West Bromwich defender Paul Scharner, which was stopped by German goalie Manuel Neuer, but the Austrians never really posed a threat.
Regularly outpaced by the quicker Germans, Austria wasted several more chances and saw a further setback when Julian Baumgartlinger earned a yellow card for bringing down Bayern Munich midfielder Thomas Müller on the half-hour mark.
Austria's first real chance came after 40 minutes with a smart interchange by Florian Klein and Erwin Hoffer that went just wide of the German goal and spurred the hosts onward.
But the Germans struck back just before half-time to take the lead with a goal by Bayern Munich's Gomez after a corner kick by club colleague Toni Kroos.
But the lead didn't last long.
Four minutes after the break, Austria equalised as German defender Arne Friedrich helped a ball by Hoffenheim midfielder David Alaba into the net. Shortly thereafter, another strike by Stefan Kulovits hit the post, sending the 47,500 fans in the packed stadium into a frenzy.
A superb run by Alaba saw his ball stopped by Neuer and a later attempt by Harnik went wide as Austria pressed for more.
At the other end, the Germans also kept Gratzei busy with a couple of close
Scharner took Austria's second yellow card of the evening, followed by Mesut Özil in the dying minutes of the game.