New Zealand were 2-75 in their second innings at stumps on day three of the clash with Australia A in Brisbane on Saturday.
Martin Guptill was 37 not out and Ross Taylor unbeaten on 14.
Test call-ups Ben Cutting (1-19) and Mitchell Starc (1-9) were the wicket takers.
The Black Caps hold an overall lead of 103 after an Ed Cowan-inspired Australia A were bowled out for 395 in their first dig earlier on Saturday.
The home side's innings was built around Cowan's knock of 145 that lasted more than seven hours.