Led by captain Kane Williamson's half-century, New Zealand extended their lead over Zimbabwe to 338 runs at tea on Tuesday's fourth day of the second Test.
After dismissing Zimbabwe earlier for 362 at Queens Sports Club in Bulawayo, the Kiwis lost two early second-innings wickets after lunch when Tom Latham (13) edged to wicketkeeper Peter Moor off Donald Tiripano.
Fellow opener Martin Guptill (11) was next out after he attempted to clear the gully area, with John Nyumbu taking the catch off Michael Chinouya.
Williamson and Ross Taylor steadied the innings with a 92-run stand for the third wicket. Williamson was undefeated on 53 while Taylor was 36 not out with New Zealand 2-118 at the break.
New Zealand declared their first innings at 4-582.