Put into bat in the penultimate match of the series, India posted 174-9 with Rinku Singh (46) and Jitesh Sharma (35) shining with the bat though they could not make the most of the final overs.
When they returned to defend, Axar Patel (3-16) wrecked Australia's top order and the tourists eventually managed 154-7 to see India grab an unassailable 3-1 lead in the five-match series.
Earlier, Yashasvi Jaiswal (37) and Ruturaj Gaikwad (32) combined in a breezy 50-run opening stand before the home side lost three quick wickets including that of skipper Suryakumar Yadav.
Rinku and Jitesh shored up India and at 129-4 after 15 overs, the home side looked poised for a late flourish that could take them near the 200-mark.
Australia, however, pulled things back in the final five overs conceding only 45 runs and claiming five wickets.
Ben Dwarshuis (3-40) struck twice in his final over and three wickets, including a run out, fell in the final over of the innings from Jason Behrendorff (2-32).
Patel fell for a first ball duck but the all-rounder decided to make amends with the ball when Australia began their chase.
The left-arm spinner dismissed opener Travis Head (31) and number four batter Aaron Hardie in his successive overs and went on to remove Ben McDermott in his final over to reduce Australia to 87-4 in the 12th over.
Matthew Wade smashed an unbeaten 36 off 23 balls but it was not enough in the end.
Both the ODI World Cup finalists had fielded second-string squads for the T20 series, which concludes in Bengaluru on Sunday.
