Batting first, the hosts were at 3/98 before the rain stopped play after only 23 overs bowled.
Jordan Gaud was unbeaten on 44 runs for the NSW XI while Nosiana Pokana (1/7), John Boge Reva (1/8) and Mahuru Dai (1/20) all picked up a wicket for the Barramundis.
Under the Duck-Worth-Lewis System, the Barramundis required 99 runs in just 15 overs.
In their pursuit, the Barramundis lost early wickets that put them deep in trouble at 4/34.
Vani Vagi Morea (22*), Mahuru Dai (16) and Dogodo Bau (10), steadied the innings to push for an unlikely victory.