The Socceroos star scored the winner in the 65th minute with the score locked at 1-1.
Matt Phillips, who was the subject of a £7 million from West Bromwich Albion earlier this month, grabbed the first goal on 19 minutes when he rounded goalkeeper Luis Zwick.
Dundee United was level on 31 minutes as Mario Bilate finished past QPR keeper Robert Green, who denied Chris Erskine late in the first half.
Charlie Austin also played the vast majority of the match in a strong Rangers side, which also included summer arrivals Jamie Mackie and Ben Gladwin, Green in goal, trialist Christopher Schorch and Asian Cup player of the tournament Luongo.
Austin has been the subject of transfer rumours after scoring 18 goals last season as QPR failed to avoid relegation to the Championship. Mile Jedinak's Crystal Palace is one club that has confirmed an interest in the 26-year-old, but Eagles co-chairman Steve Parish admitted he thinks Austin will pass up the opportunity to play at Selhurst Park and wait for a bigger club.
“There’s a good chance he will go beyond us, so to speak,” Parish told TalkSport.
