After losing captain Ajinkya Rahane (4) in the second over of the final day, Rishabh Pant gave the tourists hope with a swashbuckling innings, including 12 fours and three sixes, propelling his side to 206/3 at lunch.
But he fell agonisingly short of a hard-fought century when he found Pat Cummins at point off the bowling of Nathan Lyon on 97 from just 118 balls, his departure ending a 148-run partnership with Cheteshwar Pujara.India needed 135 runs to win when Pujara's stubborn resistance ended on 77, with Josh Hazlewood beating the bat to send the bails flying.