Luongo, 24, provided a clever pass for team-mate Conor Washington, who benefited from a defensive error from Joe Worrall before firing home a runaway goal.
The Australia midfielder has played in 34 of QPR's 45 Championship fixtures this season and the 2-0 win confirmed his side's safety for another season in England's second division.
Meanwhile, Mooy's Huddersfield hopes of a top four finish took a hit with a 2-0 defeat at relegation-threatened Birmingham City.
Terries coach David Wagner made a host of changes to his starting line-up, including Mooy starting from the bench, and the gamble didn't pay off as a gritty 10-man Birmingham side claimed a 2-0 win.
The result could have ramifications for Huddersfield, who fell to fifth with the loss, with the third and fourth-placed sides receiving the advantage of hosting the second-leg of the upcoming Championship play-offs.
Elsewhere in England, three Aussies were in action in Barnsley's 1-1 draw with Burton Albion.
The result, against compatriots Callum Elder and Ryan Williams, also sealed Jackson Irvine's Burton their survival in the Championship for next season - an impressive feat after gaining consecutive promotions during the past two campaigns.
Australia defender Bailey Wright's Bristol City pulled off the upset of the round to defeat would-be champions Brighton and Hove Albion 1-0 on their home turf, as The Robins secured their place in next season's Championship.
In Belgium, Socceroos goalkeeper Mat Ryan kept a clean sheet in Genk's 3-0 win over Kortrijk, while his Australian team-mate Mitch Langerak starred as Stuttgart claimed a 3-2 victory over Nurnberg in 2. Bundesliga.
Meanwhile, former A-League attacker Gol Gol Mebrahtu continued his impressive form, after last week's hat-trick, in Mlada Boleslav's 2-1 win over Zlin in the Czech Republic.
And in the Hungarian OTP Bank Liga, ex-A-League journeyman David Williams played the full 90 minutes as Haladas eased past Paksi 2-0.
