So Jasprit Bumrah and Bhuvneshwar Kumar are all set to win another game before the T20Is. But Finch couldn't go on as Hardik Pandya (1-14) broke the partnership in the 12th over when Jasprit Bumrah made a catch at mid off look very easy, managing to hold on and force Finch to walk back.
However, the experienced opener soon found his stride, enjoying particular success against Zampa and Head as Australia's slow bowlers struggled to make an impact.
While Rohit started cautiously, Rahane got into the action right away, flicking Pat Cummins in the opening over and punching the bowler straight behind him in his next over.
Earlier, Australia won the toss and chose to bat first.
Aaron Finch's return has given a facelift where the Australia's batting and through knocks of 124 and 94 the Victorian have something from the David Warner from his pre-Ashes slumber.
After Rahane's wicket, skipper Virat Kohli contributed with well rounded 35 runs and took India nearly to home, before both him and and Rohit fell prey to Adam Zampa.
50- The number of matches lost by Australia in India, the most they have lost overseas. Travis Head departs. The left arm spinner bowls a fuller length, Travis Head tries to go for sweep but changes his short at the last moment only to see the ball crashing onto the stumps.
Ajinkya Rahane, who is India's third choice opener, came in and filled in his boots this series with impressive performances in all the matches of the series barring the first match at Chennai.
Rohit Sharma, who scored a match-winning century in the fifth and final one-dayer against Australia here on Sunday, said the current Indian team has got an excellent bench strength which could help them touch greater heights.