Steve Smith's 20th Test century held Australia together after India debutant Kuldeep Yadav triggered a collapse on the opening day of the fourth and final match in Dharmasala.
The visiting skipper struck 111 - his third hundred of the series and seventh against India - as his side, also boosted by fifties from David Warner and Matthew Wade, posted 300.
Smith and Warner took advantage of India's sloppiness in the field to take the score to 144 for one shortly after lunch following the early departure of Matt Renshaw.
But left-arm spinner Kuldeep, replacing injured captain Virat Kohli, led the fightback by returning figures of four for 68, including three wickets during a collapse that saw Australia lose five for 64 runs in the afternoon session.
Wade thwarted India with 57 before falling shortly before the close, which arrived after India were forced to survive a testing maiden over from Josh Hazlewood.
Smith's decision to bat looked debatable when Renshaw was bowled by Umesh Yadav in the second over.
Yet the 27-year-old and Warner, dropped by Karun Nair at third slip from the first ball of the match, soon took control in a stand of 134 until Kuldeep struck in his fourth over.
Warner edged to slip for 56 and, after Umesh strangled Shaun Marsh down the leg side, Kuldeep bowled Peter Handscomb through the gate and Glenn Maxwell with a wrong'un.
Smith, having reached three figures from 150 balls, then nicked Ravi Ashwin to slip to leave the score 208 for six.
However, Wade took over the mantle, forming important partnerships with Pat Cummins, who made 21 before becoming Kuldeep's fourth victim, Steve O'Keefe and Nathan Lyon to frustrate the hosts.
Source: PA
