Finch had managed only one fifty in his previous 10 T20 Internationals and his slump has been a major talking point in the lead-up to Australia's title defence on home soil.
His 76 off 54 balls will ease some of the pressure on the under-fire opener, though it was not enough to secure victory as a spectacular late collapse gave India a six-run win.
"It's nice to get a few in the middle," Finch said afterwards at the Gabba.
"It would have been nice to get us over the line but can't win the World Cup in a practice game."
Shami, replacing the injured Jasprit Bumrah in the India squad, was summoned to bowl his only over with Australia needing 11 runs from the last six balls with four wickets in hand.
The seamer conceded two runs with each of his first two deliveries before wreaking havoc as Australia lost four wickets in four balls, including a run out.
"He's coming back after a long time, so we wanted to give him an over," Rohit said of letting Shami bowl the final over.
"We know how lethal he can be with the new ball, but we just wanted to give him a little bit of challenge coming and bowling that death over and you saw what he did."
With Australia preferring to chase, India made a competitive 186-7 with half-centuries from opener KL Rahul (57) and number four Suryakumar Yadav (50).
Rohit Sharma's 14-ball 15 would do little to ease concerns about the India captain's form heading into the tournament, while Virat Kohli (19) did not last long either.
In another practice match, last year's finalists New Zealand were bundled out for 98 runs in 17.1 overs by South Africa, who chased down the meagre target with 8.4 overs to spare.
Wayne Parnell struck twice in the powerplay before the South African spin duo of Keshav Maharaj (3-17) and Tabrazi Shamsi (2-6) ran through New Zealand's batting line up.
Only Martin Guptill (26) and Glenn Phillips (20) got into double digits for New Zealand.
