For the hosts, Mitchell Starc and Kane Richardson picked two wickets each.
In return, Australia was handed a revised target of 119 runs in 15 overs. However, just when the hosts looked comfortable after a great start with their scorecard reading 41/0 in 3.1 overs, rains forced the umpires to abandon the match.
Both the sides will now face-off in the second contest at the Manuka Oval in Canberra on Tuesday.