Travis Head and Marnus Labuschagne held their nerve on a viciously turning Indore pitch to guide Australia to a nine-wicket victory Friday and only their second Test win in India since 2004.

After Australia were thrashed in the first two Tests inside three days, the series now stands at 2-1 to the hosts with one match remaining.

Set just 76 to win, the tourists lost opener Usman Khawaja to only the second ball of the day for a duck, before Head and Labuschagne eased them to a famous triumph.

Head finished on 49 and Labuschagne was 28 not out.

The dogged victory secured Australia's berth in the ICC World Test Championship final in June at The Oval. India will be sure of their place if they win the fourth Test in Ahmedabad.

"I just tried to take it one step at a time," said Head.

"We have seen it throughout the series that with the wickets, the quality of bowling, anything can happen.

"We had to make some changes (after the earlier defeats) but I think we've done a fantastic job to come back after being under pressure in the first two games."

In a low-scoring and frenetic encounter, Australia skittled India for 109 on day one with spinner Matthew Kuhnemann giving the hosts a taste of their own medicine with five wickets.

In reply Australia made a solid start before collapsing to 197 all out before lunch on day two, their last six wickets tumbling for just 11 runs.

Eight wickets for spinner Nathan Lyon saw India bundled out for 163 in their second innings, setting up a victory target which -- on paper at least -- seemed comfortably within Australia's grasp.

But they made the worst of starts with Khawaja, the hero of the first innings, out almost immediately when he edged Ravichandran Ashwin to keeper Srikar Bharat.

A stunned Khawaja, who had looked supremely assured in the first innings, reviewed the decision but the dismissal was upheld -- to jubilation from the noisy Indore crowd.

Virat Kohli was convinced he had caught gum-chewing Labuschagne, the world number one Test batsman, at slip off Ashwin in the seventh over but India's review was unsuccessful.

After 45 minutes, Labuschagne and Head changed gears.

Head launched Ashwin for a six over mid-on and the next over drilled Ravindra Jadeja down the ground for a four as the shackles came off.

Labuschagne got in on the act, hitting Jadeja for a four and dismissing a short Ashwin delivery on a half-volley for four more to bring a rare Australia win in India in view.

A flurry of more boundaries quickly reduced the deficit and silenced the home crowd.

- 'It didn't happen' -

It is only the third time that India -- who have won their last 15 home series -- have lost a game at home in the last decade.

Skipper Rohit Sharma said his batsmen should have been more "brave", especially against Lyon.

"We wanted a few guys to stand up and put their hand up and put their hand up and take the team through, but it didn't happen," Rohit said.

"We were slightly behind and we didn't adapt as we would have liked to."

Steve Smith, captaining Australia in place of Pat Cummins, who went home to be with his ill mother, called the victory a team effort.

"Yesterday we had to toil really hard... but we really stuck at it. Nathan got all the rewards with eight wickets but I think our bowlers as a collective were really good," Smith said.

"I like captaining in this part of the world. I feel like I understand the conditions really well. It's a lot different to other parts of the world," he added.

"We fought back here and played our style for longer periods of time than we perhaps did in the first two Test matches.

"Hopefully we can put up a similar performance and finish the series really well."