Should they beat the Faroe Islands on Tuesday then Joachim Low's side will have secured their place in Brazil.
Miroslav Klose edged the hosts in front after a quiet opening half-hour scoring his 68th goal for Germany, thus equalling Gerd Muller's long-standing record.
However Austria, who came into game level on points with Sweden and Republic of Ireland in the battle for a playoff spot, almost hit back when Bayern Munich's David Alaba forced a save out of club colleague Manuel Neuer.
The German keeper was forced into action to stop Aleksandar Dragovic's goalbound effort from Alaba corner on the stroke of half time.
However, the home side made their superiority count with a vital second goal from midfielder Toni Kroos.
Thomas Muller wrapped up the victory, scoring two minutes from time to the delight of the home crowd at the Allianz Arena.
While Germany are close to qualification, defeat for Austria saw Sweden leapfrog into second in Group C after winning in Dublin.