Austin, signed from Championship rivals Burnley at the start of the month, wasted no time in scoring his first goal for the club, although there was a huge degree of fortune surrounding the goal. Just three minutes in, Jermaine Jenas' effort took a deflection off the striker and evaded Artur Krysiak in the Exeter goal.
QPR dominated the first half, with David Hoilett and Jermaine Jenas both testing keeper Krysiak.
It was another summer signing in the shape of Danny Simpson who secured the victory however, finishing with his right foot after an excellent move from the R's on 50 minutes.
Harry Redknapp's men continued to be comfortable as the home side's confidence dropped in the second-half, leaving them to cruise into the Capital One Cup second-round.
Redknapp certainly did not underestimate his League Two hosts and named a strong line up including three former England internationals in Joey Barton, Jermaine Jenas and Bobby Zamora.
However, it was new signing Austin that broke the deadlock with a goal inside three minutes of his full debut. The former Burnley frontman reacted quickest when Jenas forced a low shot goalwards as Exeter only partially cleared a corner.
Liam Sercombe's long-range shot, comfortably held by Brian Murphy, was Exeter's only attempt on target in the first half and the Devon side had goalkeeper Artur Krysiak to thank for keeping them in the game with several good saves.
Rangers added to their lead on 53 minutes when Simpson fired a low shot across goal and into the far corner, but to their credit Exeter refused to buckle and Arron Davies saw his long-range shot hit the crossbar.
Shaun Wright-Phillips also struck the woodwork for QPR after a brilliant solo run.