The visitors lost 7-69 in the first T20 global in Ranchi as they limped to 8-118 before rain ended their innings with eight balls remaining.
From there on, India took complete control of the game with Yadav and Jasprit Bumrah (2-17) among the wickets.
Australia have looked out of sorts in the limited-overs series and with the skipper being ruled out, it will be a big task for Warner to salvage some pride ahead of next month's Ashes. But soon, in-form Finch and Glenn Maxwell (17) stabilised the Australian innings and forged a 47-run partnership for the second wicket.
After thrashing Australia in 5 One Day International series, now Virat Kohli's boys are getting ready to win three-match T20 series against Kangaroos. It's that 3-0 loss that Australia will look at keenly to draw some inspiration.
Before this series, India had beaten Sri Lanka, while Australia's last T20 assignment was also against the same side; they lost 1-2 at home.
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Paceman Jason Behrendorff is likely to make his long-awaited global debut, while Andrew Tye, after replacing Pat Cummins (rested), is among four quicks in the squad.
Cricket Australia said on Saturday that cricket captain Steve Smith will return home from the team's tour of India with a right shoulder injury. The 38-year-old's his death bowling ability will be a welcome mix to the Bhuvneshwar Kumar-Jasprit Bumrah axis. However, only two spinners are likely to find a place in the playing XI.
Stand-in skipper David Warner made eight, while the injured Steve Smith ran the drinks and will return to Australia on Sunday.
Australia meanwhile recalled their T20I specialists Moises Henriques, Daniel Christian, Andrew Tye and Glenn Maxwell.
The visitors' middle-order failed once again in Ranchi as Travis Head and Moises Henriques fell cheaply to Hardik Pandya and Yadav respectively. When Kane Richardson was missing in the 5th ODI, the lack of intensity was manifested in the bowling department as spells from Cummins & Coulter Nile alone couldn't enforce the pressure on India.