Chasing a revised target of 48 runs in six overs, the hosts achieved the win with three balls to spare. Opener Shikhar Dhawan, on 15, and skipper Virat Kohli, on 22, remained unbeaten.
But it was left-arm wrist spinner Yadav who set up India's 1-0 lead in the three-match series as he returned figures of 2-16 to restrict Australia to 118-8 in 18.4 overs when rain halted play.
"It has been a combined effort of the players. But also the management group who have given great ideas in getting specialist players for formats," Kohli said at the post-match presentation.
"Giving the youngsters chances... Wrist spinners if you give them confidence, they will get hit for one game but five games they will get you wickets and turn the game around on its head," he added.
Opener Aaron Finch's 30-ball 42 was the only bright spark for the David Warner-led side. Australia were jolted ahead of the clash with regular regular skipper Steve Smith forced out of the series with a shoulder injury.
In reply, the hosts lost Rohit Sharma early after the opener was bowled by paceman Nathan Coulter-Nile for 11. He hit a four and a six during his seven-ball stay.
The left-right batting combination of Dhawan and Kohli then took the attack to the opposition as they hit six boundaries between them to ensure a big win.
- 'Better next game' -
Earlier the Indian bowlers never allowed the opposition batsmen to get going after being put into bat. Fast bowler Jasprit Bumrah backed up Yadav's efforts with two strikes.
"Bhuvi (Bhuvneshwar Kumar) and Bumrah have been brilliant in limited-overs lately. You need to be able to execute yorkers and slower balls and you need skill," said Kohli.
Warner was out in the first over after chopping a seaming delivery from Kumar onto his stumps. He made eight with the help of two boundaries.
Finch then put together a 47-run second-wicket stand with Glenn Maxwell to raise hopes of an Australian recovery but spinners soon turned on the heat.
Leg-spinner Yuzvendra Chahal got Maxwell for 17 and Yadav bowled Finch in the 10th over to rattle the visitors' top order.
Bowlers kept coming on to get wickets at regular intervals to flatten the Australian batting.
"At the end of the day, it's a poor result for us. We have to be better next game," said a disappointed Warner.
The second T20 is scheduled on Tuesday in Guwahati.