Former world junior champion Sam Webster was the best of the Kiwi contingent in the men's sprint, securing the bronze medal with two straight wins over Australian Andrew Taylor.
In the battle for the minors, Matt Archibald took out fifth from fellow Southlander Eddie Dawkins.
Earlier a powerful Australian combination was too strong for New Zealand in the under-19 4000m team pursuit, catching the Kiwis who had to settle for the silver medal.
After the first day in the men's omnium, Southlanders Pieter Bulling and Cameron Karwowski lie second and third respectively behind Australian Luke Davison.
Levin's Gemma Dudley sit in third place in the women's omnium, behind Australians Annette Edmondson and Bella King with three final disciplines today.
The final day of competition features the omnium, men's keirin, women's sprint, women's points race and men's madison
Results from day three of the Oceania track cycling championships in Adelaide last night:
Elite men:
Points race: Hayden McCormick (NZL) 53, 1; Jack Cummings (AUS) 33, 2; Mitchell Mulhurn (AUS) 32, 3.
Sprint, bronze ride: Sam Webster (NZL) bt Andrew Taylor (AUS) 2-0.
Under 19 men:
Scratch race, 10km: Regan Gough (NZL) 1, Nathan Bradshaw (AUS) 2, Alex Porter (AUS) 3.
4000m team pursuit: Australia 4:09.986, 1; New Zealand, 2 (caught).