Behrendorff, playing only his second international match, ended with dream figures of four for 21 in four overs.
The 27-year-old from Western Australia swung the ball both ways on a helping pitch with Rohit Sharma (8), Shikhar Dhawan (2) and Virat Kohli (0) among his high-profile scalps.
It was the first international 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.
Kohli departed two balls later after getting a faint inside edge while attempting a flick and the looping ball was caught by none other than the left-arm pacer.
Behrendorff then had Manish Pandey caught behind with one that swung away just enough before Dhawan fell to a spectacular running catch by opposition captain David Warner.
His spell of four overs was enough to break the backbone of Indian batting which was hardly tested in the ODI series. The figures were also Behrendorff's best in the T20 format.
However, Australia were able to tighten their noose around India in the middle overs through Adam Zampa (2/19 in four overs). He had a charging Dhoni stumped with a perfect leg-spinner before finding Jadhav's stumps to leave India in more trouble at 67 for six.
Hardik Pandya (25) hit a cracking six over midwicket, much to the entertainment of the home crowd but it was not enough to take India to a competitive total.
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