India will take a 2-1 series lead into the fifth and final match in Brisbane on Saturday after skittling Australia for 119 in their chase of 167 for eight.
Bowling for the first time in the series, Washington Sundar took 3-3 in 1.2 overs while fellow all-rounder Axar Patel had 2-20 as Australia lost their last nine wickets for 52 runs at Carrara Stadium.
Australia spinner Adam Zampa and paceman Nathan Ellis took three wickets apiece for the hosts to restrict India to what had seemed a below-par total after home captain Mitchell Marsh won the toss and elected to field.
Australia cruised past 60 for the sole loss of opener Matt Short (25) but the chase went awry as they lost 3-12 in the late-middle overs to fall to 103 for six.
Not even the recalled Glenn Maxwell could stop the rot as the pugnacious all-rounder fell for two with stumps shattered by the last ball from legspinner Varun Chakravarthy.
Patel was named man-of-the-match, having also contributed an unbeaten 21 with the bat to push India past 160.
India opener Shubman Gill top-scored with 46, anchoring top-order partnerships with Abhishek Sharma (28) and Shivam Dube (22).
While India's spinners set up the win, captain Suryakumar Yadav gave credit to the batters.
"The way Shubman and Abhishek started, they knew this was not a 200-220 wicket," he said.
"They batted very smartly. It was a complete team effort from the batters."
With the first match in Canberra having been washed out by rain, Australia can only hope to draw the series 2-2 in Brisbane.
Marsh said he thought 167 was a par score but left Australia with a few challenges.
"We failed to go over the line. Fair play to India and they are a world class team," he said.