Hosts India take a 1-0 lead in the three-match series when they enter the second Twenty20 match at the newly built Barasapara Cricket Stadium, then they will have to take the invincible lead in the series.
The final game will be played in Hyderabad on Friday.
The very next over, Aaron Finch, who made eight runs, was walking back to the pavilion as he suffered the same fate as Warner, but only off the bowling of Kumar.
After faltering with the bat, the Indian bowlers put up an ordinary performance, offering too many loose balls to Head and Henriques.
Rohit Sharma made 11 off seven balls before Nathan Coulter-Nile found a way through his defences to claim the only wicket of the innings.
But India's hopes of defending a small target were dashed as their spinners, Kuldeep Yadav (0-46) and Yuzvendra Chahal (0-29), struggled in dewy conditions. Henriques came and showed his experience. Brilliant start from Behrendorff, he has taken three wickets so far in only two overs splashing out just 12 runs.
"Test cricket is the ultimate prize and wearing the baggy green cap is something I'm sure all cricketers aspire to - I certainly do", Behrendorff said after cleaning up the entire Indian top order of Rohit Sharma, Virat Kohli, Shikhar Dhawan and Manish Pandey.
It was the first global game played at the venue and the packed crowd was in for a shock after Rohit hit two crisp fours in the opening over bowled by Behrendorff.
Bowling at up to 140kmh, Behrendorff not only troubled the Indians with his swing but also with the sharp lift he earns off a length.
Continuing which his fantastic spell, Behrendorff got the other Indian opener, Shikhar Dhawan, in his third over and the fifth of the Australian innings. Spinners dominate the shortest format and no bowler is more valuable than a good wrist spinner.
Mahendra Singh Dhoni and Kedar Jadhav offered some resistance with a fifth-wicket stand of 33 before Adam Zampa had the former stumped for 13 and clean bowled the latter for 27.
When will the 2nd T20 between India and Australia be played?
India on the other hand, failed to get going with Dhoni being stumped for the first time in a T20 global after adding 33 runs for the fifth wicket with Jadhav.