After Dwyer's goal, it remained 0-1 till the 51st minute when Thomas Craig made it 2-0. The Black Sticks responded with Hugo Inglis firing it in from a tight angle on the baseline.
The Kiwis sniffed a chance and continued to work in the last five minutes of the game, but it was Glenn Turner who sealed it with a diving goal in the 57th minute to end it 3-1.
Although the Black Sticks Men are still to face Fiji on Saturday, they are eyeing the final game of the tournament which will be played at 4pm this Sunday. A tournament win would book the Black Sticks Men a spot at the 2016 Rio Olympics.
"We are clear that we just need to forget the occasion and go out and play - we have a lot to gain from the game and that's how we will approach it," said Batch.
In the earlier games, Fiji Men walloped Samoa 20-0 and Australia Women stormed to a 25-0 win against Samoa in their opening game of the tournament.
Tomorrow is a rest day for all teams. The Black Sticks Women face Australia at 2pm on Saturday and the Black Sticks Men play Fiji at midday on Saturday.
Click here for more information on the 2015 Oceania Cup. Tickets are cheaper to purchase online than at the gate.
The final men's and women's games are live on Sky, with all other games livestreamed on www.hockeynz.co.nz
RESULTS
Black Sticks Men vs Australia
Full time: 1-3 (Australia win)
Half time: 0-1
NZ goal scorers: Hugo Inglis
Australia goal scorers: Jamie Dwyer, Thomas Craig, Glenn Turner
Fiji Men vs Samoa
Full time: 20-0 (Fiji win)
Half time: 13-0
Fiji goal scorers: Amenatave Veitamana, Adrian Smith, Alsace Smith, James Saqacala x2, Adrian Smith x2, Martin Fong x2, Leevan Dutta x8, Adrian Smith, Jerome Edwards x2
Australia Women vs Samoa
Full time: 25-0 (Australia win)
Half time: 18-0
Australia goal scorers: Jodie Kenny x3, Ashleigh Nelson x3, Laura Barden x2, Stephanie Kershaw, Emily Smith x4, Jane-Anne Claxton x2, Anna Flanagan, Brooke Peris x3, Madonna Blyth, Karri McMahon, Georgina Morgan, Madison Fitzpatrick x2, Mariah Williams