Battling half-centuries from Peter Handscomb and Shaun Marsh helped Australia secure a draw in Ranchi and take their series against India into the final Test still all square at 1-1.
Australia 1st inns: 451 (Smith 178*, Maxwell 104; Jadeja 5-124, Yadav 3-106)
India 1st inns: 603-9 dec (Pujara 202, Saha 117, Vijay 82, Rahul 67, Jadeja 54*; Cummins 4-106, O'Keefe 3-199)
Australia 2nd inns: 204-6 (Handscomb 72*, March 53; Jadeja 4-54)
Match drawn - four-match series level at 1-1
Battling half-centuries from Peter Handscomb (pictured) and Shaun Marsh helped Australia secure a draw in Ranchi and take their series against India into the final Test still all square at 1-1.
Handscomb (72no) and Marsh (53) joined forces at a highly-vulnerable 63 for four when their captain Steve Smith fell shortly before lunch in the third Test.
But still 89 runs away from making their hosts bat again at that stage, they responded with a stand of 124 which shut India out for more than 62 overs on the way to 204 for six at stumps as the stalemate was agreed 10 minutes from the scheduled close.
The tourists had resumed initially on 23 for two on the last morning and, after an encouraging start, in the space of four balls lost Matt Renshaw lbw to Ishant Sharma from round the wicket and then Smith - to a misjudgment, bowled off-stump trying to pad away Ravi Jadeja.
The left-arm spinner finished with figures of four for 54 from a marathon 44 overs, and nine wickets in the match.
But Australia's fifth-wicket pair held sway. They each had a DRS lbw scare shortly before their 50s, Handscomb surviving on 44 against Umesh Yadav and Marsh on 48 against Ravi Ashwin.
Otherwise they were chanceless, Handscomb finishing unbeaten after keeping out 200 balls in all.
Despite Marsh's eventual departure to a short-leg catch off Jadeja and Glenn Maxwell's bat-pad to Ashwin, both teams can therefore still win the series when it concludes in Dharamsala next week.
India subjected Australia to a day of unrewarding toil in Ranchi, with a double century for Cheteshwar Pujara and a hundred from Wriddhiman Saha on day four of the third Test.
The pair shared a 199-run stand as the touring attack failed to take a wicket in either the morning or afternoon sessions.
Pujara's 202, compiled over 525 deliveries, was the third double hundred of his career and second against the Baggy Greens, while Saha's third Test ton provided steely support.
India resumed 91 runs shy of Australia's first-innings but declared with a healthy advantage at 603 for nine, and then struck twice to leave the tourists wobbling.
Ravindra Jadeja, having earlier chipped in with 54 not out, was responsible for both, bowling David Warner in the sixth over and then sending back nightwatchman Nathan Lyon to bring on stumps.
A score of 23 for two, and a deficit of 129 going into the final day, leaves India pushing for a victory that had once seemed highly improbable.
Australia will have plenty of tired legs in the pavilion, with Steve O'Keefe having sent down a mammoth 77 overs, returning a manful three for 199, while seamers Josh Hazlewood and Pat Cummins bowled 44 and 39 respectively.
Matt Renshaw will restart on seven not out, with captain Steve Smith due to join him.
Cheteshwar Pujara batted throughout the day to reach his 11th Test century as India battled for parity on the third day of the third Test in Ranchi.
Pat Cummins provided a constant threat for Australia, finishing with four for 59, but could not breach the defence of Pujara, who ended unbeaten on 130 as India reached 360 for six at the close, still 91 runs behind the tourists' total of 451.
Murali Vijay (82) helped put on a partnership of 102 for the second wicket with Pujara before some hostile bowling from Cummins, in his first Test for six years, dragged Australia back into the contest.
Starting the day on 120 for one, the home side made comfortable progress through the morning session, but were fortunate not to lose two quick wickets shortly after the drinks break.
Pujara was the beneficiary of a marginal lbw call, prompting Australia to review unsuccessfully as Steven O'Keefe looked to have beaten the inside edge of the bat, only for replays to prove inconclusive before the original decision was upheld.
That was Australia's second unsuccessful review of the innings, and they were made to rue their wastefulness with the very next delivery as Vijay edged the ball onto his pad and was caught at short-leg off Nathan Lyon, only for the umpire to wave the appeals away.
O'Keefe finally made the breakthrough the ball before the lunch break, tempting Vijay to wander down the pitch before missing a straight ball to allow Matthew Wade to smartly whip off the bails.
Kohli's miserable series continued as he drove loosely at Cummins shortly after the new ball was taken, edging to Steve Smith at second slip for six to give the tourists some momentum and leaving the Indian skipper with just 46 runs in the series.
Ajinkya Rahane made 14 before becoming Cummins' third victim, before Josh Hazlewood jagged one back to bowl Karun Nair for 23 as Pujara battled on at the other end, reaching three figures from 214 balls in a trademark gritty knock.
Cummins produced a rip-snorter to have Ravi Ashwin caught behind as Australia tightened the screw in a final session, but Saha and Pujara saw India through to stumps with the match evenly poised.
Steve Smith's unbeaten 178 and a maiden Test century for Glenn Maxwell boosted Australia to a competitive total but India responded well in Ranchi.
Smith recorded his best score in Asia and his masterful innings, along with Maxwell's 104, lifted the tourists to 451 all out on day two of the third Test, with Ravindra Jadeja finishing as the pick of the bowlers with five for 124.
India, in response, closed on 120 for one as Pat Cummins marked his return to Test cricket with the wicket of KL Rahul, who feathered behind to depart for a well-crafted 67.
Rahul had been the aggressor in a 91-run opening stand although he and Murali Vijay, back in the team for his 50th Test after missing out in Bangalore because of a shoulder injury, did not take many risks.
Rahul brought up his fourth fifty in five innings although once again he could not convert as he nicked behind to Matthew Wade to give Cummins his first Test wicket since November 2011.
Cummins' express pace in only his second Test gave the Indian batsmen pause for thought but he could not make another breakthrough as Vijay (42no) and Cheteshwar Pujara (10no) survived to the close.
Their efforts gave India captain Virat Kohli another night to rest a shoulder injury he sustained while diving to prevent a boundary on the opening day.
He did not take to the field on Friday morning as opposite number Smith, a centurion on Thursday, and Maxwell set about swelling Australia's total, resuming on 299 for four.
After seeing his bat break off the first ball of the morning, Maxwell survived a couple of nervy moments to bring up three figures, reaching the landmark with a slash between two slips that flew away for his ninth four.
Maxwell was dismissed three overs later, though, ending a 191-run partnership with Smith, after edging behind off Jadeja, who saw off Wade in an identical manner after a quickfire 37 before bowling Cummins two balls later.
Smith remained untroubled, however, effortlessly moving to his 150 and he received capable support from Steve O'Keefe (25) to take Australia well beyond 400.
Jadeja had his fifth when Lyon fended to silly point while the slow left armer executed a superb 'no-look' run out of Josh Hazlewood to end Australia's innings as Smith, who struck 17 fours in his 361-ball knock, was denied the chance of reaching his double century.
Australia captain Steve Smith responded to the controversy surrounding him since the second Test with India by making an unbeaten century on day one of the third Test in Ranchi.
Smith's conduct was questioned by India skipper Virat Kohli after the former appeared to look to Australia's dressing room for advice over reviewing an lbw decision against him on the last day of the hosts' series-levelling win.
The International Cricket Council took no action against Smith but the two countries' boards nevertheless felt the need to meet to resolve the issue.
Smith, who on the eve of this match criticised Kohli's comments, made good on his decision to bat first with 117 of 299 for four. It was his 19th Test ton and second of the series, passing team-mate David Warner's 18 and matching the mark of Australia legends Mark Taylor and Mike Hussey.
Smith shared an unbroken stand of 159 with Glenn Maxwell, whose 82 including two sixes comfortably beat his previous Test-best of 37.
At stumps Smith told Sky Sports 2: "You can't control the past, that's gone. You've got to let that go as quickly as you can. Obviously I came out and said 'I made a mistake' at the end of the last game and moved on from it. It was about focusing on this Test match in Ranchi."
Smith and Maxwell joined forces at 140 for four after most of the top order had failed to build on starts. Opener Matt Renshaw's 44 was the best score after the fifth-wicket pair's efforts.
Australia earlier handed paceman Pat Cummins a second Test cap, more than five years after his first, in place of the injured Mitchell Starc while India replaced out-of-form opening batsman Abhinav Mukund with Murali Vijay.