Put into bat, Australia overcame a poor start to reach 132 for seven in 19 overs when rain forced the players off the field at the Melbourne Cricket Ground.
Ben McDermott made 32 not out off 30 balls before scurrying off the ground with batting partner Andrew Tye.
The umpires first considered a 19-overs-a-side game before setting India a revised target of 90 from 11 overs to level the series.
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However, with the rain returning, the match was eventually called off.
Australia, who clinched the rain-hit series opener in Brisbane, will carry a 1-0 lead into Sunday's final match in Sydney.
(Reporting by Amlan Chakraborty in New Delhi; editing by Toby Davis)
