India, chasing 287 runs for victory, were dismissed for 140 in the second test match at Perth.
Australia beat India by 146 runs before lunch on the fifth and final day of the second test on Tuesday to level up the four-match series at 1-1.
The tourists, chasing 287 runs for victory, were dismissed for 140 at the new Perth Stadium when Jasprit Bumrah was caught and bowled by quick Pat Cummins.
It was a first win in eight test matches for Australia.
India, who won the opener at Adelaide Oval by 31 runs, have never won a test series in Australia.
Left-arm paceman Mitchell Starc finished with 3-46, while spinner Nathan Lyon took 3-39 on a feisty pitch. For India, Ajinkya Rahane made 30 with the bat and Rishabh Pant also 30.
Spinner Nathan Lyon claimed the prized wicket of Indian captain Virat Kohli.
Lyon dismissed Kohli for the seventh time in Test cricket, two more than any other bowler, when he had him caught at slip by Usman Khawaja for 17.
Kohli was unable to repeat the heroics of his first innings century, the ball catching the outside edge as he probed forward defensively.
His departure was the cause of great delight for Australian captain Tim Paine, after the pair had exchanged words at the conclusion of the third day.
The Australian wicketkeeper, looking for his first win as skipper in five Tests since taking over from the disgraced Steve Smith, celebrated the dismissal with a cheeky comment to not out batsman Murali Vijay.
“Murali, I know he’s your captain. But you can’t seriously like him as a bloke...”— Vithushan Ehantharajah (@Vitu_E) December 17, 2018
Areas, Tim Paine. #AusvInd #Kohli pic.twitter.com/sDc85Yj3Rv
"Murali, I know he's your captain, but you can't seriously like him as a bloke," Paine said, in comments picked up by microphone.
The series continues with the Boxing Day test at Melbourne Cricket Ground starting on December 26 before concluding with the fourth test in Sydney in the New Year.