India won the first Test against Australia at the Adelaide Oval on Monday by 31 runs.
Australia were all out on 291 in their second innings.
R Ashwin took the last wicket to take a 1-0 lead in the four-match series.
This is the first time that India won an opening Test of a series in Australia.
Previously, India removed Travis Head and Shaun Marsh in the first session of the fifth and final day to close in on victory.
With Hazlewood’s wicket, Australia were bowled out for 291 and India took a 1-0 series lead.
Australia were chasing 323 runs to win and had begun the day from overnight 104/4.
Post this win, Virat Kohli became the first Indian captain to win Tests in Australia, England and South Africa. India also became the second Asian side to win the first Test of a series in Australia. India’s Cheteshwar Pujara was declared man of the match. Ashwin, who took six wickets, registered his best match figures in Australia.
BCCI tweeted, “#TeamIndia has done it! Another glorious chapter added to our love affair with Adelaide. Got close in the end, but India win by 31 runs and lead the series 1-0 #AUSvIND.”
“History repeats itself! In the 2003 Adelaide Test, No. 3 Rahul Dravid won the Player of the Match. In 2018, No. 3 @cheteshwar1 is named Player of the Match. #TeamIndia,” BCCI added.