Finch smashed seven boundaries and a six in his 116 balls knock.
India are slowly returning to the match as they took two quick wickets of Glenn Maxwell (23) and Finch.
Umesh Yadav has taken three wickets so far.
Australia have lost the wickets of David Warner (12), Steve Smith (105) , Maxwell (23) and Finch.
Shane Watson (2*) and Michael Clarke (3*) are currently at the crease as Australia scored 239 runs for the loss of four wickets after 40 overs.
Australia earlier won the toss and decided to bat first.
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