Bhuvneshwar Kumar, Hardik Pandya and Yuzvendra Chahal picked up a wicket apiece, putting India in a commanding position in the first of the three-match T20I series before rain played spoilsport in the 19th over the innings.
India had few problems in a run chase reduced to six overs, Rohit Sharma the only wicket to fall as he was bowled by Coulter-Nile for 11.
During his second over, Kuldeep provided the most decisive moment in the match.
Smith, who made a significant impact during Australia's 2-1 Test loss against India in March, has struggled to match up his form in the limited-overs format. Not only this, they lost four of these matches on Australian soil.
India won the toss in 1st T20 match and chose to field first.
Stand-in skipper David Warner made eight, while the injured Steve Smith ran the drinks and will return to Australia on Sunday. In an era of flat tracks and shortened boundaries, a bowling attack has to possess an exotic element to clinch white-ball matches.
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"I thought after we got off to a pretty good start with the bat, obviously losing our way through the middle order again", Finch said. There was variable bounce and negotiating that was a headache for the Australians.
Conditions: The city has seen heavy rainfall over the last couple of days and the outfield and the pitch have been covered a lot of the time.
Australia hardly provided any resistance after that.
Ranchi: India have managed to scalp three wickets wickets; courtesy Bhuvneshwar Kumar, Yuzvendra Chahal and Kuldeep Yadav; at the end of ten over. Australia capitulated in the death overs and it was only the rain that stopped the carnage.
After an nearly two-hour delay, the match resumed. It had to be a silly question as this lineup has proven themselves capable of chasing down the biggest of targets.
The Nawab of Najafgarh also reckoned that with opener Shikhar Dhawan, who is back in the side after a short break, will get a chance to open the innings alongwith Rohit Sharma. A run out appeal on Virat Kohli just a couple of balls later only aggravated those worries.