India have taken a 1-0 lead in the much-anticipated four-match series against Australia (AP Photo)

India ended a 10-year-wait for a Test win Down Under as Virat Kohli's visiting team outplayed Australia by 31 runs in the first of the ongoing four-match series in Adelaide.

The Asian giants last won in Australia under Anil Kumble at Perth during their trip Down Under in 2007-08. They were blanked 4-0 under MS Dhoni in 2011-12 and suffered a 2-0 defeat during the 2014-15 tour despite Kohli scoring a truckload of runs.

India had failed to seize crunch moments in the opening Tests during their two previous overseas tours of the year in South Africa and England but Kohli's men made sure they ended up third time lucky on Monday, defending a 323-run target successfully despite a heroic effort from Nathan Lyon who gave India a few nervous moments towards the end.

With the win, India also went up 1-0 in a Test series for the first time in Australia, ending a 70-year long drought.

Kohli has also become the first Asian captain to win Tests in Australia, South Africa, and England. India had won the Johannesburg Test against the Proteas in January this year following which they defeated England in the fourth Test of a five-match series at Southampton later in August-September.

India have also become the first team to win a Test match in Australia, England and South Africa in the same calendar year.

Australia, who resumed the final day of the riveting Test match at 104 for four, faced an uphill task as no team had successfully chased more than 315 at the Adelaide Oval. The India bowlers made life even more difficult for the hosts as they came out determined and patient, striking at regular intervals.

Shaun Marsh gave India looked solid in the morning session as he notched up a half-century but Jasprit Bumrah removed the veteran and helped go into the Lunch break with optimism and relief. Earlier in the day, Ishant Sharma had local favourite Travis Head and Australia's first-innings star caught for 14.

The historic victory was set up by Cheteshwar Pujara, whose first innings 123 provided India with a score strong enough to fight after a poor batting performance by the top order. The bowlers then struck at regular intervals to hand India a slender 15-run lead.

Cheteshwar Puajra slammed a century in the first innings and followed it up with a half-century in the second in Adelaide (AP Photo)

R Ashwin spun a web around Australia's batsmen while Jasprit Bumrah rattled the hosts with his pace. Ishant Sharma and Mohammed Shami chipped in with key wickets to ensure India stayed in the game.

India batted much better in the second innings. Pujara had conceded his top order should have done better on the first day and they listened to his call - KL Rahul scored a fluent 44, Kohli was patient for his 34 while Ajinkya Rahane scored 70 and shared a key 87-run stand with Pujara, who made 71 to go with his 123.

Though the lower order imploded, India still managed to set Australia a 323-run target. On the fourth day, Mohammed Shami and Ashwin picked two wickets apiece to leave Australia in a tough spot.

Aaron Finch, Marcus Harris, Usman Khawaja, and Peter Handscomb were dismissed before stumps on the penultimate day.

An absolute brute from Ishant Sharma had India up and about early on day five.#AUSvIND | @Toyota_Aus pic.twitter.com/QPR1SOz69a cricket.com.au (@cricketcomau) December 10, 2018

Australia would have hoped for a bit of fight from their overnight batsmen Marsh and Head but that was not to be. Captain Tim Paine looked resolute but once he was dismissed for 41, the writing was on the wall for Australia.

Lyon, who shone with the ball, came up with a spirited effort in the end, collecting an unbeaten 38 off 47 balls to give Kohli a few nervous moments on the field. He had stitched a 32-run stand with No. 11 Josh Hazlewood before Ashwin snapped the stand and helped India clinch the historic win.

Also See: