The Premier League newcomers were without both of their close-season signings, Rio Ferdinand and Steven Caulker, for the clash in Germany but Austin's 21st-minute header secured victory.
Harry Redknapp was able to welcome back Alejandro Faurlin and Esteban Granero to the starting line-up following troublesome knee injuries last season, with both midfielders comfortably completing 45 minutes.
Austin posed the greatest threat and could have given his side the lead in the opening 10 minutes as he rose to meet a right-wing cross, but the 25-year-old had made his move too soon and was flagged offside.
There was nothing wrong with his effort midway through the first half, though, as he met Joey Barton's pinpoint free-kick to head into the top corner.
The goal only served to spark Rot-Weiss into life as Christian Falk was denied on three occasions by the impressive Rob Green.
With 11 changes at half-time it took QPR time to settle back into the match and their hosts applied a little more pressure after the hour.
Substitute goalkeeper Joe Lumley carried on Green's good work with two goal-saving blocks, while Clint Hill was on hand to deny the hosts with a well-executed challenge in the 69th minute.
The visitors rarely threatened after the break and visibly began to tire in the closing stages as the tempo dropped.