New Zealand were 2-75 in their second innings at stumps on day three of the clash with Australia A in Brisbane.
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.
He shared a 150-run fifth wicket stand with wicketkeeper Matt Wade (53).
Cowan resumed at 60 not out on Saturday.
His marathon innings included 25 fours.
But it was not enough to earn a Test nod - the vacant opener's position went to his Australia A team-mate David Warner when the team for next week's Gabba Test was named on Saturday.
Doug Bracewell took 4-87 for New Zealand, backing up from his brutal unbeaten 73 in the Black Caps' first dig of 423.
