After Neil Wagner had removed Chamu Chibhabha 40 minutes before the close of play, Trent Boult and Tim Southee grabbed two wickets in the final three balls of the day to send Zimbabwe to stumps on 58 for three in pursuit of an improbable 387 for victory.
After bowling Zimbabwe out for 362 in their first innings to a earn a 220-run lead, New Zealand opted against enforcing the follow-on and instead spent the afternoon building a formidable target.
Although openers Chibhabha and Tino Mawoyo made a promising start in reaching 45 without loss, three dismissals before the close left Zimbabwe facing a long final day to avoid defeat.
"We are pretty confident that we can bat for the day," Zimbabwe's batting coach Lance Klusener said. "They've been in the field for a long time. From a team growth point of view, I am looking forward to it."
Having gone to his maiden Test hundred and reached 115 on day three, Ervine extended his knock on the fourth morning before finally holing out at the end of Zimbabwe's innings.
"Craig was really organised. He had a good plan and he knew what he wanted to do," said Klusener.
"That's where we need to get to with the other batsmen. It's one thing having a plan, but it's important to be comfortable with the plan. It was nice to see the reward that he got from a lot of hard work."
West Indian Rohan Kanhai, South African Kepler Wessels and India's Virat Kohli were the other three.
Meanwhile Taylor continued his remarkable series with the bat, making 67 not out to take his series tally to 364 runs without being dismissed.
New Zealand declared shortly after tea to begin their push for victory, and will go into the final day confident of clinching a 2-0 series victory.
"There are a couple of deliveries going over the top and a few staying quite low. Hopefully it deteriorates a little more on day five.
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