The tourists had made a flying start to contest after being put in to bat at the toss, reaching 97-1 when play was eventually called off for the last time.
Abhishek Sharma was the only wicket to fall to seamer Nathan Ellis with Shubman Gill unbeaten on 37 off 20 balls and captain Suryakumar Yadav 39 not out from 24 deliveries.
The second game of the five-match series takes place on Friday in Melbourne.
India are missing allrounder Nitish Kumar Reddy for next two matches due to back stiffness while Shreyas Iyer is still recovering from injury.
India secured a 2-1 victory in their five-match T20I series against Australia after the final match at the Gabba in Brisbane was abandoned due to heavy rain and lightning on Saturday.
India fought back to bowl Australia out to win the fourth T20I and take an unbeatable 2-1 lead in the five-match series in Carrara on Thursday.
Rishabh Pant has recovered from injury and has been included in India's Test squad for the two-match series at home against the Proteas that starts in Kolkata on 14 November.
Jake Weatherald has received his maiden international call-up as Australia named a 15-man squad for the first Ashes Test against England, starting on 21 November in Perth.
