Wellington's fellow spinner Jess Jonassen was also a standout and conceded just three runs from her opening two overs. She finished with 0-15 from four overs while Kristen Beams took 2-21.
In response though, Australia's top order stumbled to 9-5 after 4.5 overs, cruelling any chance of victory.
Only two Australians made double-figure scores - Alex Blackwell (30no) and Alyssa Healy (12).
The top order collapse was rapid: after Beth Mooney was run out on the fourth ball, the hosts lost their next four wickets in 11 balls.
The initial five batters dismissed made just eight runs between them. And the entire innings lasted just 16 overs.
Holly Huddleston was New Zealand's best bowlers with figures of 2-9 from four overs, while Lea Tahuhu (2-13) and 16-year-old schoolgirl Amelia Kerr (2-16) also performed well.
- AAP and NZ Herald