In-form duo New Zealand Kane Williamson and Ross Taylor made unbeaten half-centuries, to leave and Zimbabwe facing a 2-0 series defeat after losing late wickets on day four of the second Test in Bulawayo.
Black Caps captain Williamson (68 not out) and former skipper Taylor (67no) hit tons in the first innings and dished out more punishment to the Zimbabwe attack on Tuesday before the declaration came on 166-2.
Ish Sodhi (4-60) got rid of Craig Ervine for a magnificent Test-best 146 as Zimbabwe were bowled out for 362 in reply to 582-4 declared and the hosts were reduced to 58-3 at stumps in their second innings, needing a highly unlikely 329 to draw the series on the final day at Queens Sports Club.
After resuming on 306-5 on the penultimate day, Zimbabwe were relying on the lower order to provide some support for Ervine but they were soon seven down when captain Graeme Cremer (8) was trapped leg before by Trent Boult (1-45).
Ervine was watchful, but helped himself to a couple of boundaries off Tim Southee (1-73) before the innings was over when he tried one shot too many and was caught at long-off in the same over in which he launched spinner Sodhi over the ropes.
Donald Tiripano and John Nyumbu had also been dismissed prior to the end of Ervine's 272-ball knock - which included 18 fours as well as that six.
Williamson opted against enforcing the follow-on and combined with Taylor for another assault on the Zimbabwe bowlers, putting on 140 after Tom Latham (13) and Martin Guptill (11) fell cheaply.
Taylor was at his sublime best and has scored 364 runs without being dismissed in this series after smashing three sixes in a well-paced 78-ball knock, while Williamson was immovable as the runs came all too easily.
Guptill dropped Chamu Chibhabha (21) in the slips, but held on to another chance to get rid of the opener off Neil Wagner (1-21) before Boult (1-11) trapped Tino Mawoyo (35) in front and Southee (1-18) ousted Sikandar Raza without scoring with what proved to be the last ball of the day.