Three-times European champions Germany are clear at the top of Group A with eight wins out of eight matches so far and cannot be caught as they seek to become the first German team to win all their matches in a qualifying campaign.
Austria are stuck on seven points from seven games in fourth place behind Turkey on 13 and Belgium on 12 from eight games.
Germany visit Turkey on October 7 and host Belgium in their final qualifier four days later as they seek a 100 percent record.
Germany got off to a flying start with Miroslav Klose scoring after nine minutes when he got a slight deflection on a shot by Ozil from the edge of the box for his 62nd goal in 111 internationals.
Klose, 33, is now just six goals short of equalling Gerd Muller's Germany record of 68 international goals, though the former Bayern Munich striker needed just 62 matches.
The imperious Ozil combined with Klose to add the second goal in the 23rd after rounding the keeper before Lukas Podolski struck a powerful left-footer five minutes later for a 3-0 lead.
"We played an amazing qualification [campaign] and we could not have qualified earlier than today," coach Joachim Low told reporters.
"But we need to keep up the pressure in the team. This is how I like my team to play. I prefer to have more action up front and if you play like you can sometimes let a goal in."
This is exactly what happened three minutes before the break when Austria's Marko Arnautovic, recalled after being dropped several months ago following a row with team mates, headed in a Florian Klein cross to cut the deficit.
Martin Harnik also scored for the visitors minutes after Ozil had restored Germany's three-goal lead with another deflected effort from the left in the 47th.
But it was Germany's night and substitutes Andre Schuerrle and Mario Gotze, with a well-timed volley, wrapped up a seventh straight win over Austria with two goals in the last six minutes as the fans in the Schalke arena stood to applaud Low's team.
"It does not matter who scores, whether it was Miroslav or me in the first goal, we had a super performance," said Ozil.
"I am delighted to have scored but first of all I am satisfied by our team performance."
For Austria, it was another disappointing campaign that could end with coach Didi Constantini leaving.
"Obviously, when a team loses the coach is the first one to be blamed," Austria captain Christian Fuchs told reporters.
"But we made our own life hard with far too many mistakes. You cannot play like that against Germany."
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