Shikhar Dhawan's hopes of landing the knockout punch were dashed due to a finger injury, but he was still padded up, just in case he had to go out as India, cautious not to falter chasing the small target, briefly suggested they might have left it for too late.
Australia pace spearhead Peter Siddle's bustling pace and consistency was holding back the batsmen from giving the charge.
In the end, Ravindra Jadeja landed two hefty blows to end Siddle's threat before skipper MS Dhoni knocked off three fours in a row against Mitchell Starc to clinch victory, with just over two overs to be bowled in the match.
India had sealed a comprehensive six-wicket victory in the third Test in Mohali to clinch the series 3-0 and annex the Border-Gavaskar Trophy with a game left.
Australia, who have looked increasingly dispirited on the tour, suddenly found the kind of collective determination that had been sorely missing in the series.
Aussie skipper Michael Clarke, nursing a dodgy back, found in Siddle a willing workhorse. The rest of the bowlers rallied around him as Clarke crowded the batsman with close-in fielders and posted men on both sides to cut off singles.
In 2011, in the final Test in Dominica, Dhoni had jettisoned a sporting chase of 180 and instead settled for a draw, attracting a lot of criticism.
Then India were just 1-0 up and it would make no sense if the batting collapsed and India lost, was his defence.
On Monday, with Dhawan out of action, he was cautious, as he did not want to give Australia any hope of a win to come back in the series.
India, chasing 133 for victory at close to five runs per over, eventually finished on 136 for four with just 2.3 overs left in the match, wrapping up the match in four days after the first day's play was washed out.
Cheteshwar Pujara (28) opened with Murali Vijay (26) and Virat Kohli (34) and Sachin Tendulkar (21) then pushed the score along but the pressure told when Tendulkar was run out to a brilliant effort by David Warner.
It was a tortuous day of cricket. Although some dust came off the pitch, it was not one of the treacherous last day surfaces.
It demanded patience from the spinners and they eventually bowled out Australia, 91 behind in the first innings, for 223 late into the afternoon session.
Brad Haddin, Mitchell Starc and Xavier Doherty --- all lucky to be playing --- kept up the fight by adding 80 runs for the last two wickets, batting for nearly two hours, facing 34.2 overs.
Seamer Bhuvneshwar Kumar, who took three wickets to give India victory hopes overnight, was kept away from the attack as he felt he would have only conceded runs with the old ball as there was not much help from the pitch.
Dubious umpiring has only added to the absence of the Decision Review System, which the Indian board opposes.
Top order batsman Phil Hughes finally made a fighting 69 but was given out leg before to Ravichandran Ashwin by umpire Aleem Dar. TV replays showed the ball was going down the leg side.
Skipper Michael Clarke, in pain, batted at No 6, scoring 18 in nearly one hour. Ravindra Jadeja dismissed him for the fifth time in six innings but there was doubt whether it was off a no ball.
The third umpire ruled it was a legal delivery, although TV replays suggested the decision could have gone either way.
Jadeja's three wickets proved crucial, highlighting the importance of newcomers in the resurgence of India.