Pace bowler Josh Hazlewood grabbed six wickets as India dramatically collapsed to 274 all out in their second innings, leaving Australia a target of 188 to win the second Test.
Hazlewood notched career-best figures of 6-67 while left-arm quick bowler Mitchell Starc and left-arm spinner Steve O'Keefe took two wickets apiece each as India folded on the fourth morning in Bangalore.
India, who resumed the day on 213 for four, started steadily with overnight batsmen Cheteshwar Pujara and Ajinkya Rahane extending their stand to 118 for the fifth wicket.
Rahane, who reached his 11th Test fifty with a boundary off Starc, and Pujara handled the spinners with relative comfort early on.
But upon taking the second new ball saw Starc and Hazlewood tore through India's batting with a burst of four wickets in nine balls.
Rahane was first to go, trapped lbw by Starc on a successful Australia review after being given not out on the field.
A fired-up Starc then shattered Karun Nair's stumps next ball with a full, in-swinging delivery and was only denied his hat-trick when Wriddhiman Saha managed to avoid a being out lbw by getting a thick edge on another full delivery that was hooping in towards middle stump.
Hazlewood got in on the action in next over, snaring the key wicket of Pujara as the batsman failed to handle a short, rising delivery and lobbed a catch to Mitchell Marsh in the gully.
Three balls later Hazlewood bowled Ravichandran Ashwin for his fifth scalp of the innings and in His next opver Hazlewood induced Umesh Yadav to loft a drive to mid-off as India collapsed from 238 for four to 258 for nine.
Saha, who finished unbeaten on 20, managed to eke out a 16-run last-wicket partnership with Ishant Sharma before O'Keefe struck on the stroke of lunch as India were all out for 274, after having resumed the day at 213 for four.
Steve Smith's Australia lead the four-match series 1-0.