Travis Head departed for 90 but his century stand with Marnus Labuschagne powered Australia to a second-innings lead against India as the fourth Test moved towards a likely draw on Monday's day five.

Axar Patel broke the 139-run partnership after he bowled Head to deny the opener a century in the second session at the world's biggest cricket stadium in Ahmedabad.

Even before the result was determined, India qualified for the World Test Championship final after New Zealand edged out Sri Lanka by two wickets in a final-ball thriller in the opening Test in Christchurch.

Rohit Sharma's Indian team will take on Australia in the title clash at The Oval on June 7-11.

Australia reached 158-2 at tea, a lead of 67, with Labuschagne (56) and stand-in-skipper Steve Smith (0) batting at the break.

Australia lost nightwatchman Matthew Kuhnemann for six off spinner Ravichandran Ashwin early in the morning session, but Head and Labuschagne stood firm with half-centuries until Axar struck with his 50th Test wicket.

Regular opener Usman Khawaja was yet to bat with "lower leg soreness" after getting hurt while fielding on day four.

India, who lead 2-1 and need a win or draw to clinch the four-match series, rode on Virat Kohli's epic 186 to post 571 all out on day four and build a lead of 91 against Australia's 480 in the first innings.

Kohli was the last man out after Shreyas Iyer did not bat due to lower back pain and the team said Monday that he will take no further part in this Test.

The pitch in the run-filled match has been vastly different from the viciously turning tracks in the opening three Tests, which all ended inside three days.