Darcy Graham’s 63rd-minute try sealed the win for the young Scots in a gripping match at the AJ Bell Stadium.
John Dalziel’s side face England next, at Manchester City’s academy ground on Saturday.
Scotland have already beaten England in this season’s Under-20 Six Nations game and will go into the match with great confidence.
indiscipline costs the Australians dear in Salford and they played most of the second half with 14 men after centre Campbell Magnay was shown a red card for picking up a second yellow in the 44th minute.
His first offence came as early as the fifth minute when he was sin-binned for a dangerous tackle.
Scotland’s Adam Hastings put Scotland ahead with an 18-th minute penalty but Australia hit back six minutes later with a try from lock Izack Rodda, which Mack Mason converted.
The Aussies led 7-3 at the break but the game swung Scotland’s way following Magnay’s dismissal. Two minutes later Zander Fagerson powered over for a try to edge Scotland a point ahead. Hastings missed the conversion.
Mason put Australia back in front 11-7 with a penalty but with 17 minutes to go winger Graham sped through the Aussie defence and touched down for the winning try which Hastings converted from the touchline.