In a clash delayed due to a wet outfield and reduced to 23 overs per side, five-time champions Australia rode on opener Smith's 55 and Cameron Green's 34 lower down to post 166-7.
But rain returned with the Netherlands in trouble at 84-6 from 14.2 overs and the game was eventually called off.
The Dutch, who are set to appear at a fifth World Cup and their first since 2011, were rattled as Starc (3-18) removed Max O'Dowd and Wesley Barresi in the final two deliveries of the opening over and castled Bas de Leede in his next.
All three batsmen fell for first-ball ducks as Starc showed no signs of rust having recently returned to the starting eleven following a groin injury.
Earlier, the match between hosts India and defending World Cup champions England in Guwahati was abandoned without a ball being bowled.
India skipper Rohit Sharma won the toss and opted to bat but rain came down shortly after and prevented play at the Barsapara Cricket Stadium in northeastern India.
England may well not mind, however, after spending nearly 38 hours travelling from London to Guwahati with lengthy layovers in between.
"We're a little bit stiff, it was a long journey," England pacer Mark Wood said on Star Sports shortly after the toss. "But this is the start of the World Cup, so we're all excited."
England will get a chance to fine-tune their skills with a clash against Bangladesh on Monday, ahead of their tournament opener on Thursday when Jos Buttler's side will meet 2019 runners-up New Zealand in Ahmedabad.
"These games are just about building up to the opening game, and we need to be ready for that one," Wood said.
India take on the Netherlands on Tuesday before heading into the showpiece event, where they are targeting their third title.
