Moises Henriques (8) went to pavilion in the 13th over after a delivery of Kuldeep Yadav hit stumps.
"It was unfortunate for Shikhar Dhawan to miss out on so many games, but he's back and even this innings of 15 will give him confidence".
Virat Kohli: There's a bit of weather around, so we would like to know where we are placed.
India will look to maintain their dominance of the hapless Aussies in the three-match T20 series and pocket the shortest version 3-0 of which they are fully capable of as evident from the Tests and the recently concluded One-Day International (ODI) series.
However, having reached 76-2 in the 10th over, the visitors struggled to up the ante on a slow, low pitch once opener Finch was bowled by Kuldeep Yadav for 42.
Earlier, after winning the toss and put being into bat, Australia made 118 for the loss of 8 wickets in 18.4 overs before the heavens opened.
By picking up the two wickets, Bumrah broke a record by going past Ashish Nehra to become the second highest wicket-taker for India in T20I's.
With a staggering 9-4 head-to-head record in favour of the hosts, and a 3-0 clean sweep in their previous meeting in Australia in January a year ago, India definitely look a formidable unit going into Saturday's encounter at the Jharkhand Cricket Association (JCA) International Stadium.
Australia skipper Steve Smith has returned home after suffering a shoulder injury during the final ODI against the same opponent.
Australia included Moises Henriques, Daniel Christian and Andrew Tye in its team.
On the other hand, India will look to continue their dominance after a thumping win over Australia in the ODI series.
Kohli announced two changes in the playing XI from the last game - Kuldeep Yadav replaced Axar Patel and Shikhar Dhawan came in place of Ajinkya Rahane.