Australia, winning the toss and electing to bat first in the match, scored 348/8 in their 50 overs.
Finch scored 107 runs from 107 balls with the help of nine boundaries and two sixes. David Warner also scored 93 runs from 92 balls which included 12 fours and a six.
Finch and Warner put up an opening stand of 187 before Ishant Sharma provided the breakthrough for India in the 30th over.
Captain Steve Smith as scored a fifty as he made 51 runs from 29 balls with the help of four fours and three sixes whereas Glenn Maxwell made 41 runs from 21 balls with six fours and a six to his name.
Sharma grabbed four wickets while Umesh Yadav sent three batsmen back into the pavilion.
The Indian side was bowled out on 323 in 49.2 overs.
Openers Rohit Sharma and Shikhar Dhawan put up an opening stand of 65 runs before Kane Richardson had the right hander caught behind after he made 41 for the team.
After Sharma’s departure, Virat Kohli came into bat and the two Indian batsmen hit the Australian bowlers to all corners of the ground.
With the 277/2 on the board and Kohli and Dhawan’s 212 run partnership, the match was seemingly going in their favor when John Hastings struck by getting the left arm batsman caught out by George Bailey. He scored 126 runs from 113 balls which included 14 boundaries and two sixes.
After Dhawan’s departure, wickets continued to fall in regular fashion for the visitors. India became 278/4 as Hasting dismissed captain M.S. Dhoni on a duck whereas Kohli was dismissed after scoring 106 from 92 balls from Richardson’s bowling.
Australia then made it 294/6 as Gurkeerat Singh was dismissed by Nathan Lyon after scoring five runs while Ajinkya Rahane became Richardson’s third victim of the match.
Richardson five wicket haul came when he dismissed Rishi Dhawan on nine and Bhuvneshwar Kumar on two runs.
Mitchell Marsh ended the proceedings as he dismissed tail-enders Umesh Yadav scored two runs in the match and Ishant Sharma to wrap up the win for the side.
Kane Richardson was named the Player of the Match.
Australia leads the five match ODI series 4-0. The fifth and final ODI will be played on 23rd January, 2016 at the Sydney Cricket Ground.