Leg-spinners Paul Strang and Adam Huckle took a wicket apiece as New Zealand lost two wickets in the space of five balls to lurch to 64 for 2 in the 22nd over when bad light stopped play, still 338 runs behind.
First Craig Spearman was caught behind for 33 by Andy Flower after offering a fine edge to Kent's Paul Strang with the score on 63 for 1.
In the next over, with only one run added, Matt Horne tried to leave a ball which reared into him and got a glove on its way to wicketkeeper Flower.
However, shortly after captain Stephen Fleming joined Pocock at the wicket, they accepted the umpires' offer for bad light and trooped off much to the disgust of the home team. Blair Pocock was unbeaten on 30 at the close.
Zimbabwe had declared their second innings on 311 for 9, leaving the Kiwis 403 to win in 126 overs.
Opener Grant Flower was their mainstay as he became the first Zimbabwean to score a century in each innings, following up his 104 in the first innings with a resolute 151 in the second.
However, Flower - who batted 334 minutes, faced 239 balls and hit 12 fours and a six for his third Test century - was given two lives, at 132 and 142.
He also became the highest run scorer for his country, overtaking Dave Houghton, who had led before the Test began with 1,396 runs. He now has 1,430 from 23 Tests.
In the morning session he and Gavin Rennie completed a Zimbabwean first- wicket record partnership of 156 as Rennie celebrated his Test debut with a half-century.
But after Flower's dismissal Zimbabwe lost wickets at regular intervals, the last six falling for just 59 runs.
Second day; New Zealand won toss
ZIMBABWE - First innings 298 (G W Flower 104; C Cairns 5-50)
NEW ZEALAND - First Innings 207
ZIMBABWE - Second innings
(Overnight: 115 for 0
G Rennie c Harris b O'Connor 57
G Flower c Fleming b O'Connor 151
A Flower c Parore b O'Connor 20
G Whittal run out 4
A Campbell c Fleming b Davis 21
D Houghton c Davis b Astle 1
H Streak run out 0
P Strang c Horne b Davis 17
J Rennie not out 16
B Strang not out 4
Total (for 9 dec) 311
Fall of wickets: 1-156 2-218 3-231 4-263 5-264 6-290 7-290 8-290 9-311.
Bowling: O'Connor 26-3-73-3; Davis 13-2-45-2; Cairns 9-0-44-0; Vettori 13-2-40-0; Harris 5-3-11-0; Astle 25.5-2-86-2
NEW ZEALAND - Second Innings
B Pocock not out 30
C Spearman c Andy Flower b Huckle 33
M Horne c Andy Flower b Paul Strang 0
*S Fleming not out 0
Total (for 2) 64
Fall of wickets: 1-63 2-64.
Bowling: Streak 5-1-14-0; Bryan Strang 6-2-15-0; Whittall 4-1-14-0; Paul Strang 4.2-1-8-1; Huckle 2-0-12-1.Reuse content