After two days of ebbing fortunes in the finale of an evenly-matched series tied at 1-1, India finally surged ahead in the morning session when they fashioned a valuable 32-run lead before they were dismissed for 332 on the stroke of lunch.
On the liveliest of the four pitches used in the series, Australia's struggles against the bouncing ball was evident as they slumped to a perilous 92 for five at tea at the Himachal Pradesh Cricket Association Stadium.
Glenn Maxwell was unbeaten on 37 at the break with Australia looking completely out of sorts after a top-order meltdown.
Karun Nair spilled David Warner at slip off Bhuvneshwar Kumar for the second time in the match but the opener, who has managed just one fifty in the series, was unable to capitalise and was caught behind for six off paceman Umesh Yadav.
Much depended on skipper Steve Smith and the highest scorer of the series hit three delectable boundaries before guiding a Kumar delivery onto his stumps to depart for 17.
Umesh then had Matt Renshaw caught behind as Australia lost three wickets before they had wiped out India's first innings lead.
The home spinners then took over with Ravichandran Ashwin dismissing Peter Handscomb and Ravindra Jadeja accounting for Shaun Marsh as Australia limped to a 60-run lead by the interval.
Earlier, Jadeja made 63 and featured in a 96-run partnership with wicketkeeper Wriddhiman Saha after India resumed 52 runs adrift and with four wickets in hand.
Jadeja started his eventful morning by being given out caught behind off the first ball of the day from Pat Cummins and the batsman, then on 16, called for an immediate review to prolong his innings when replays suggested no bat was involved.
The 28-year-old duly brought up his fifty and celebrated it with his trademark twirl of the bat held like a sword.
He was also hit on the helmet after deflecting a ball from Cummins, who peppered the batsman with short deliveries. Jadeja connected on one of them to slog his fourth six before dragging a delivery from the same bowler on to his stumps.
Steve O'Keefe then sent back Kumar in the next over and Cummins (3-94) got rid of Saha, who made 31, with another short delivery.
Off-spinner Nathan Lyon (5-92) dismissed debutant Kuldeep Yadav for seven to wrap up the India innings and complete his second five-wicket haul of the series.
(Editing by John O'Brien)
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