Socceroos midfielder Mark Bresciano opened the scoring in the 17th minute with a thunderous volley from distance before Rhodes, making his first start after a substitute appearance against Cyprus last year, levelled in the 28th minute with a diving header from a Danny Fox cross.
Australia substitute Jason Davidson put through his own goal with a header from a Fox cross in the 63rd minute before Scotland substitute Ross McCormack, who had replaced Rhodes, stretched the home side's lead in the 76th minute with a drive from the edge of the box.
Asked if his goal was a dream come true, the 22-year-old Huddersfield player said: "Absolutely. You dream of starting for your country and walking out in front of the fans and hearing the national anthem.
"It gave me goose bumps before the start of the match and it was a fantastic feeling.
"I am delighted. I didn't know too much about it at the time but it was a good delivery in by Danny Fox and I was delighted to see it go in.
"I tried to get myself in the position where the ball might drop and sometimes as a striker it does go in."
Scotland begin their 2014 World Cup qualifying campaign with a double-header against Serbia and Macedonia at Hampden next month.
Rhodes, however, was reluctant to assume he would still be in Craig Levein's squad.
He said: "I don't know about that. There are so many good strikers and so many good players for the manager to choose from.
"That will be his decision and I will concentrate on going back to Huddersfield Town and giving my all for them.
"Tonight there were some okay bits and some bits I need to learn from.
"But I am young enough and hopefully in years to come I might be able to adapt to the situation but the senior players like Gary Caldwell helped me tonight."