New Zealand took three wickets in the last two overs to leave Zimbabwe struggling in its second innings at 58-3 at stumps Tuesday in the second test.
Set a daunting target of 387 to win at Queens Sports Club, Zimbabwe collapsed from 45-0 on the fourth day - losing both openers Chamu Chibhabha (21) and Tino Mawoyo (35), along with Sikandar Raza for a duck.
Earlier, New Zealand made its second declaration of the match on 166-2 after Zimbabwe had resumed its first innings on 305-6 before being dismissed for 362.
Kiwi captain Kane Williamson was undefeated on 68 while Ross Taylor was 67 not out. The tourists lost openers Tim Latham (13) and Martin Guptill (11).
"There were too many soft dismissals in the first innings and looking back I think there were a couple of soft dismissals again (in the second)," said Zimbabwe's batting coach Lance Klusener.