Ben Campbell shot even par and the third counting score came from one of Ryan Fox (76) or Vaughan McCall (76).
New Zealand manager Brent Paterson believed his side's total was only disappointing because it looked paltry compared to Australia.
"We started slowly and the Australians came out hot,'' he said. "We deteriorated in the middle but we came back pretty strongly to post a good score of even par - the same score as yesterday. But two of the Australians have played unbelievable golf and we are now 14 shots back on them and have some work ahead of us.''
Perry, the New Zealand Amateur champion, was sure they still could deliver a memorable come-from-behind win.
"We've seen some good scoring today so we know that it is out there, we just need three or four them tomorrow,'' he said. "We need to be attacking to go low and we'll see what happens.''
Australia, the Trans Tasman Cup, Nomura Cup and Southern Cross Cup champions, will go into the final round as hot favourites to claim another piece of silverware.
South Africa remained in third by one shot from Argentina, 13 shots back from New Zealand.
The Four Nations Cup is an amalgamation of two tournaments the Four Nations (between New Zealand, Australia, Japan and Canada) and the Southern Cross Cup (between New Zealand, Australia, South Africa and Argentina) becoming one strokeplay event.