India, who won the opener at Adelaide Oval by 31 runs, have never won a test series in Australia.
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.
The series continues with the Boxing Day test at Melbourne Cricket Ground starting on Dec 26 before concluding with the fourth test in Sydney in the New Year.