Australia was set to play the Philippines in the second game of a day-night doubleheader.
Unsworth, a 23-year-old right-hander who reached Double-A last season, induced 15 ground balls and retired the first 11 New Zealanders he faced. He struck out the side in his final inning.
The winner from the four-team Sydney tournament, which ends Sunday, will qualify for next year's 16-team World Baseball Classic.
South Africa crushes New Zealand by 159 runs in 3rd ODI
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