Steve Smith became the first Australian skipper to score three centuries in a series in India before debutant Kuldeep Yadav pegged back the tourists in the fourth Test on Saturday.
Smith smashed 14 fours in his scintillating 111-run knock to take Australia to 208-6 at tea on the opening day of the series-deciding finale at Dharamsala.
The 27-year-old also became only the second visiting captain to hit three hundreds in a series in India after England's Alastair Cook.
Smith's dismissal shortly before tea tilted the scales in favour of India, who must win the match to regain the Border-Gavaskar trophy.
India's ploy to keep chinaman bowler Kuldeep under wraps and use him only for the final Test paid dividends as he caught the Aussies by surprise through his guile and unorthodox spin.
Paceman Umesh Yadav also tasted success, having picked two wickets for 54 runs so far on a track that is hosting its first-ever Test.
The visitors were cruising at 144-1 before India's bowlers hit back to grab five wickets in the post-lunch session.
Kuldeep picked his first international wicket when he had David Warner caught by stand-in skipper Ajinkya Rahane in the slips for 56.
The bowler broke down as he hugged his teammates to celebrate the occasion.
Kuldeep struck again soon to send back Peter Handscomb (eight) with a ball that turned in sharply and hit the stumps.
Smith put on 134 runs for the second wicket with Warner after Australia lost opener Matt Renshaw in the second over of the day.
Smith's efforts meant he remained on top of the batting chart in the series with a whopping 482 runs from seven innings.
The unassuming captain underlined his reputation as the world number one Test batsman, reaching his 20th century in the process.
The skipper raised his bat and helmet to acknowledge the standing ovation from a grateful Australian dressing room.
He finally lost his wicket to spinner Ravichandran Ashwin, with Rahane taking another catch in the slip region.
Smith's run in the series has been in contrast to his opposite number Virat Kohli who was forced to sit out of the game with a shoulder injury.
As a batsman, Kohli has had a series to forget, having managed only 46 runs from three Tests.
Before this game, Kohli played 54 Tests on the trot without missing a match since November 2011.