Defending a total of 328/7, the youngsters bowled out Australia for 228, registering their first victory.
India picked up wickets at regular intervals, with Shivam Mavi and Kamlesh Nagarkoti taking three wickets each.
For Australia, opening batsman Jack Edwards (73) was the highest run-scorer.
He also picked up four wickets for 65 runs.
The openers, Shaw and Manjot Kalra led India's surge from the front.
Both the batsmen, however, started cautiously, playing out the first six overs for just 27 runs.
It was a six from Shaw which opened the floodgates for India.
After that, both the players changed their gear and took on the Aussie bowling attack as India crossed the 50-run mark in the 10th over.
However, both Kalra and Shaw missed out on individual centuries.
Shaw was dismissed on 94 when he edged the ball to the keeper, while Kalra was caught at mid-wicket and was dismissed at 86.
Prithvi Shaw was crowned the man of the match for his knock of 94.
India are the three-time world champions, with the last victory coming in 2014.
They are in Group-B alongside Australia, Zimbabwe, and Papua New Guinea.
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