Cheteshwar Pujara claimed his first century on Australian soil to rescue India from a top-order collapse and leave honours even on day one of the opening Test.
Favourites heading into the Adelaide clash, India – who won the toss and elected to bat – struggled to settle early on, a string of loose shots seeing Australia claim four wickets before lunch.
Even the world's best Test batsman Virat Kohli was unable to make an impact, Usman Khawaja producing a sensational one-handed diving catch to remove the Indian skipper for three.
That left India reeling and 19-3 became 86-5, but Australia did not have it all their own way as a superb 123 from Pujara lifted the tourists to a respectable 250-9 before he was superbly run out by Pat Cummins from what proved to be the final ball of the day.
Australia were back on home soil for a Test without Steve Smith and David Warner for the first time since the star pair were handed 12-month bans following the Cape Town ball tampering scandal in March.
They started well with Josh Hazlewood (2-52) striking the first blow in just the second over with a full delivery to KL Rahul (2), who loosely edged through to Aaron Finch.
Another poor shot and a lack of footwork brought the innings of Murali Vijay (11) to a close as Mitchell Starc's delivery and Tim Paine's catch helped reduce India to 15-2 before a moment of magic from Khawaja claimed the prized scalp of captain Kohli.
Fielding at gully, Khawaja – who endured a difficult build-up to the Test following the arrest of his brother on Tuesday – dived to his left and hung onto a stunning catch after Kohli pushed at Cummins (2-49).
India went from 19-3 to 41-4 when a late swinging but wide delivery from Hazlewood drew an edge from Ajinkya Rahane (13) as the tourists stumbled to lunch.
Nathan Lyon (2-83) took over in the middle session with two wickets, aided by some erratic batting from Rohit Sharma (37), who had targeted the Australian off-spinner.
After slog-sweeping Lyon for six in the 38th over, Rohit attempted the same shot off the very next ball but top-edged to debutant Marcus Harris before the spinner dismissed Rishabh Pant (25) caught behind.
While all around him were losing their heads, Pujara remained calm and composed and with the support of Ravichandran Ashwin (25) he steadied the ship with a 62-run stand for the seventh wicket.
Pujara was watchful throughout, punishing the bad balls off the back foot and keeping his nerve when he moved into the 90s – successive pulls for six and four off Hazlewood moving him onto 99 and beyond 5,000 Test runs after Starc (2-63) had cleaned up Ishant Sharma (4).
He reached three figures for the 16th time in his career soon after but he could not make the close unbeaten as Cummins' sensational throw at one stump from a fully horizontal mid-air position caught him short of his ground.