New Zealand resumed overnight on 92-0 and eased past Zimbabwe’s first innings total of 149 before their innings ended on 307-9, with all-rounder Nathan Smith retiring hurt with an abdominal strain.
Zimbabwe, who then had to face 13 overs in the final session on Thursday, lost openers Ben Curran and Brian Bennett cheaply and were 31-2 at the close, still trailing by 127 runs.
Opener Devon Conway top-scored for New Zealand with 88 but went early after lunch as he cut a sharply rising delivery from Tanaka Chivanga to Brian Bennett in the gully.
Daryl Mitchell was bowled for 80 by Newman Nyamhuri, the last wicket to fall as New Zealand added 215 to their overnight score for a significant lead on a testing pitch.
Will Young had been dismissed first ball of the day for 41 by Blessing Muzarabani, who returned Zimbabwe’s best bowling figures of 3-73 off 26 overs.
Henry Nicholls scored 34 while Smith made 22 before being forced from the crease in obvious pain.
Zimbabwe will resume on Friday with Nick Welch (2 not out) and Vincent Masekesa, who had yet to score, at the crease.