Shubman Gill then hammered home the advantage with 63 runs off 54 balls with six boundaries and a six.
Shaw struck eight fours and two sixes off 100 balls and Kalra slammed 12 fours and one six as the two bettered a 14-year-old record for India.
India made the ideal start to their ICC Under-19 Cricket World Cup 2018 campaign with a clinical performance as they beat Australia by 100 runs in their opening fixture.More news: Kane tipped to break record
In their turn at the wicket, Australia lost wickets at regular intervals to be dismissed for 228.
For Australia, opener Jack Edwards top-scored with 73 while wicket-keeper batsman Baxter J Holt put in a rear-guard effort of 39 of 30 deliveries. He put on 57 runs for the first wicket with Max Bryant (29) and 60 runs for the third wicket with Jonathan Merlo (38).
While Dravid, who has been at the helm of U-19 and India A squad for some time, may not like to focus on individuals, it is very hard to not see the likes of skipper Prithvi Shaw as the a vital cog in the team's batting wheel.
"We've been playing some very good cricket of late, so rather than focusing on individuals and naming a few people, at this age we really believe that every one of these kids is talented". Our mind was clear - just wait for the loose balls.More news: Former Blackhawk Phillip Danault hit in head by Zdeno Chara slap shot
Lakshan later said he had not been bothered by the fall of early wickets and praised his captain.
Don't miss England's Under-19 World Cup opener, against Namibia, live from 9.25pm on Sunday night on Sky Sports Cricket (channel 404) and Sky Sports Mix (channel 121).
Raynard van Tonder's player-of-the-match knock of 143 anchored South Africa to a mammoth 7-341, with the skipper compiling a 125-run partnership with Jiveshan Pillay (62) for the second wicket.
Kenya battled gamely through to 7-172 off their 50 overs.More news: Xbox One Outsold PS4 in December 2017