Winger Louis Lynagh, the son of Wallabies great Michael, scored a try on debut as Italy beat the championship-chasing Scots 31-29 in Rome on Saturday to secure a first home win in the Six Nations for 11 years.
The Wallabies won only two of nine tests under Eddie Jones last season and crashed out of the pool stage of the World Cup for the first time after losses to Fiji and Wales.
Australia next play in July when they host the eighth-ranked Welsh for two tests and Georgia for one in their first outings under new coach Joe Schmidt.
There have been a few glimmers of hope for Australian rugby in the first three rounds of the new season of Super Rugby Pacific, where wins over the dominant New Zealand teams have been rare in recent seasons.
The New South Wales Waratahs stunned the reigning champion Canterbury Crusaders in round two and a Queensland Reds side featuring another of Lynagh's sons, flyhalf Tom, upset the pacesetting Waikato Chiefs in Brisbane last weekend.
The All Blacks remain in third place in the rankings behind world champions South Africa and Ireland despite England's Six Nations win over the latter at the weekend.
New Zealand play England twice at home and Fiji in San Diego in July.
