when he joined the Gunners from Real Madrid for 50 million euros (US$65.9m) on Monday.
"We're delighted with the result, we scored some nice goals going forward and were tight at the back."
Veteran striker Miroslav Klose equalled Gerd Mueller's 39-year-old record of 68 goals for Germany when he scored in the 33rd minute before Toni Kroos and Thomas Mueller's second-half goals kept Germany in charge of European qualifying Group C.
"I can't really be compared to Gerd Mueller, I have taken more than twice as many games as him to score the goals," said Klose modestly on his 129th appearance, while Mueller, now 67, needed just 62 matches to score his goals for West Germany.
Coach Joachim Loew was a relieved figure on the sidelines at Munich's Allianz Arena as his side left the Austrians goalless having leaked nine goals in their three previous friendly games.
"We had a bit more time to work together this week and we did our homework," said Loew, who picked up his 65th victory in his 96th international as coach.
"We knew the way Austria would play and we took the sting out of their tail.
"Our defence worked well and it pleased me that we kept them goalless, but the main thing is the victory.
"The result gives us a bit more security at the top of the group.
"I am pleased that Miro Klose finally got his goal and the subject is finally closed.
"I am sure he will go onto score his 69th goal."
Goal-scorer Thomas Mueller said the team were delighted with the result.
"We didn't leave much at the back and that feels good, but we need to be more consistent," said the 23-year-old Bayern Munich star.
Victory gave Loew's side their sixth win from their seven qualifiers with only last October's dramatic 4-all draw with Sweden in Berlin -- when Germany threw away a 4-0 lead -- the only blot.
The defeat leaves Austria third in the group, three points behind Sweden, who moved up to second after beating the Republic of Ireland 2-1 in Dublin on Friday.
Germany are away to Group C bottom side Faroe Islands on Tuesday, the same night Austria host the Republic of Ireland in Vienna.