Finch, who helped the visitors make an imposing 200-plus total at Rajkot in the tour-opening one-off T20 International, was again in attacking form with a well-made 72 off 79 balls with eight fours and three sixes after Australia opted to bat.
Finch and fellow opener Phil Hugues (47) got Australia off to a solid start with 110-run opening stand before India fought back through their left-arm spin twins Ravindra Jadeja (1 for 35) and Yuvraj Singh (2 for 34).
James Faulkner (27 off 22 balls) struck breezily towards the end to help the visitors cross the 300-mark after a mid-innings stutter.
The Indian bowlers, barring Jadeja and Yuvraj, looked off colour, particularly Ishant Sharma (1 for 56), who just like in the T20 game, gave away lot of runs for a late wicket.
Even the ground fielding left a lot to be desired.
Australia, who set the hosts a target at an asking rate of 6.1, made a very cautious start, with openers Finch and Hugues preferring to adopt the wait and watch policy in the first few overs before opening out.
The first five overs produced only 13 runs but the sixth bowled by Bhuvneshwar gave the Aussies the chance to accelerate as Finch took the attack to him and carted him for a six over the straight field and two fours -- a cover drive and a pull.
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