David Warner will now lead Australia againt Virat Kohli's men in the T20I series. Rain came down after Australia had limped to 118 for 8 in 18.4 overs, and by the time it subsided, India's chase had been shortened to six overs.
After loosing the series of 50 overs match by 4-1, Indian cricket team earned first place in the worldwide ODI rankings.
India have made two changes to their side from the ODI series against Australia. Then rain stopped the match.
With Australia reeling at 76/3 in 9.5 overs, the Indian bowlers took full advantage of the wicket and conditions and didn't let any Aussie batsman get settled in the middle.
Finch's cameo was ended by some handsome bowling from Yadav after the Aussie opener was clean bowled attempting to sweep a full and quicker delivery for a 30-ball 42.
Australia's captain Steve Smith is expected to be fit for the Ashes despite returning home from the tour of India with a shoulder problem.
Who Planned the Assassination of Kim Jong-un's Half-Brother?
Prosecutors at Malaysia's High Court were seeking to establish the basic facts regarding Kim Jong Nam's death on February 13 . In that time, Kim Jong-nam, the estranged brother of North Korean leader Kim Jong-un, grew increasingly desperate for help.
Meanwhile, the next match of the series will be played in Guwahati on Tuesday.
After a 4-1 defeat to India in the One-Day International series, the onus is on Australia to not let the hosts get on a roll again.
Uncapped left-arm speedster Jason Behrendorff, along with wicketkeeper-batsman Tim Paine, all-rounders Moises Henriques and Dan Christian, are the new additions in Australia's T20I squad.
The star batsman - who has not played a T20 for his country since March 2016 - was in doubt after hurting his shoulder during the fifth and final one-day worldwide against India last week.
The visitors could manage to add only 42 runs in the next 8.5 overs losing another five wickets before rain interrupted play. Jasprit Bumrah meanwhile had figures of 2 for 17 in the 3 overs he bowled. The final contest of the series will be on Friday in Hyderabad.