India took a 2-1 lead in the four-match Test series after beating Australia by 137 runs in the third test in Melbourne on Sunday.
India will retain the Border-Gavaskar trophy even if the series is drawn level at Sydney as they have won the previous series at home in 2017.
The first session of the fifth day was washed out and it took only 27 balls in the second session for India to take the final two Australian wickets. Jasprit Bumrah and Ishant Sharma completed the formalities in what turned out to be the 150th Test win for the Indian team.
Australia was all out for 261 in 89.3 overs and India won the test match at MCG after 37 long years.
Jasprit Bumrah was named the player of the match for his stupendous figures of 9-86.