The hosts warm up for their upcoming World Cup 2014 qualification double-header against Serbia and Macedonia by coming from behind to beat the Socceroos at Easter Road
Craig Levein handed Huddersfield Town's Rhodes his first competitive start for his country, while managerial counterpart Holger Osieck named Aston Villa new-boy Brett Holman in his starting XI.
The hosts started the brighter of the two sides with an early chance dropping to Rhodes but the forward failed to get his positioning right to get the shot in.
However it was the Socceroos who broke the deadlock in the 18th minute of the match. An attack down their left ended with Robbie Krause firing a shot on goal which Danny Fox handled, with replays showing that the ball had already crossed the line.
Despite the appeals, the referee waved play on and the ball went behind for a corner, which was only cleared as far as Bresciano, who unleashed a spectacular shot from 25 yards out which flew past Allan McGregor in goal.
An equaliser arrived 10 minutes later when Fox got forward well and whipped in a cross which was met by Rhodes with a bullet header which flew into the back of the net.
Both sides enjoyed spells of possession but failed to create any more chances with the scoreline all-square at the interval.
The second half started in a brisk, open fashion as both sets of players pushed for a goal and it almost went the way of the visitors with Luke Wilkshire forcing substitute goalkeeper Matt Gilks into a smart save.
Scotland found themselves in front three minutes later courtesy of a Davidson own goal. The 21-year-old had only just come onto the pitch before heading Fox's cross into the back of the net.
Levein's side extended their lead in the 75th minute when McCormack picked up the ball after a Sasa Ognenovski error before wrong-footing Adam Federici with a smart finish which would have impressed his manager.
Next up for Scotland is a World Cup 2014 qualification double-header against Serbia and Macedonia.