The Huddersfield striker marked his first start with his first senior goal for the national team at Easter Road.
Rhodes was given the nod to lead the line, with Miller rested for the friendly following his move to Vancouver Whitecaps.
But the veteran forward looks set to be back at the forefront of Levein's plans for next month's World Cup qualifiers against Serbia and Macedonia.
Levein said: "I would say just now that Kenny is the number one striker at this minute in time.
"He has proven over a period of time that he can score goals on big occasions.
"We don't have a great amount of strikers available so it was an ideal opportunity to see Jordan.
"After one game, he will still have to be a little bit patient."
Rhodes cancelled out an impressive opener from Mark Bresciano, before an own goal from Jason Davidson put the Scots ahead and Ross McCormack sealed the victory.
On Rhodes - who netted 40 club goals and eight for Scotland's under-21 side last season - Levein added: "You don't like to put any pressure on a young guy making his starting debut in international football.
"But he kind of put the pressure on himself with his record of scoring goals. He handled it extremely well."
Levein was also pleased with skipper for the night Gary Caldwell, who anchored the midfield against the Socceroos.
He said: "You put him at centre-back and he plays well, you put him in central midfield and he plays well.
"He's a great passer of the ball. Most importantly, he's somebody other players look to and get inspired by.
"I was really pleased but in no way surprised by his performance."
As well as sweating over an injury to goalkeeper Allan McGregor, a positive night for the Scots was marred when Ian Black was booed by home fans when he made his debut late on.
Levein put the incident down to a former Hearts player being jeered by Hibernian fans at Easter Road.
He joked: "These Hibs supporters, eh?
"I just think that's what it is. We are at Easter Road and he was a Hearts player for a long time.
"Probably every time he comes here it's the same."
