The two sides managed just one win between them in their three games each in pool play earlier in the week, and will now challenge for the fifth to eighth placings.
The victory went to the women's team when they beat hosts Otago 3-2 on Tuesday.
With goals to New Zealand representative and former Iona College pupil Olivia Shannon, Grace Gibson, and Emma Jackson, the win followed the side being beaten 5-1 by North Harbour in the first round on Sunday, and 2-1 by Auckland on Monday.
The men's team were beaten 3-1 by North Harbour, 6-2 by Canterbury and 5-1 by Otago.
After a one-day break the men play Waikato today while the women play Wellington. On Friday the men play Manawatū and the women play Waikato.