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Luongo, who joined the club in June from Swindon Town, bagged the winner on 65 minutes with a long-range header at the Hive Stadium home of Barnet FC.
Matty Phillips opened the scoring for QPR with United equalising through courtesy of Mario Bilate.
Rangers kick off their Championship campaign in two and a half weeks with manager Chris Ramsey describing the game as a "worthwhile" hit-out.
The Socceroos next play on September 3 in a World Cup qualifier in Perth.