Manjot Kalra's unbeaten century anchored his side's win, reaching his century off 101 balls, and included eight fours and three sixes.
India bowled Australia out for 216 in 47.2 overs, as seamers Ishan Porel and Kamlesh Nagarkoti and spinners Anukul Roy and Shiva Singh all took two wickets apiece.
In slightly overcast conditions, Australia won the toss and opted to bat but found themselves 59-3, as seamer Porel dismissed openers Jack Edwards (28) and Max Bryant (14) before Nagarkoti had captain Jason Sangha (13) caught behind.
Jonathan Merlo (76) and Param Uppal (34) shared a 75-run fourth-wicket partnership but Roy struck twice to break the back of Australia's resistance, taking a brilliant caught-and-bowled to dismiss the Uppal before Merlo's attempted reverse sweep saw him caught at cover.
Nagarkoti and Shivam Mavi, who will both feature in this year's IPL which will be showed live on Sky Sports from April 7, mopped the tail with 16 balls of Australia's innings remaining.
India, who went unbeaten throughout the entire tournament, began confidently but captain Pawan Shaw (29) was bowled by Will Sutherland to give Australia hope.
Shubman Gill, who will play for the Kolkata Knight Riders in the IPL, failed to reach his half-century for the first time in the tournament as he was bowled by Uppal but Kalra remained unnerved.
The 19-year-old shared an unbroken 89-run third-wicket stand with Harvik Desai (47), with the wicketkeeper hitting the winning boundary to spark wild celebrations from the Indian team at the Bay Oval.