Opener Devon Conway (79) and nightwatchman Jacob Duffy (eight) were unbeaten at stumps on Thursday as New Zealand led by 49 runs.
Conway and Will Young put on 162 for the first wicket before Young chopped on a delivery from Trevor Gwandu to be bowled for 74 just before the close.
Matt Henry, man of the match in New Zealand's comprehensive first-Test win, bagged another five-wicket haul with 5-40 in 15 overs while debutant Zakary Foulkes took 4-38 after Zimbabwe had won the toss and decided to bat.
Brendan Taylor top scored for Zimbabwe with 44, falling just when he looked on course for a successful return to the team at the age of 39.
He was back after serving a three-and-a-half-year ban for breaching anti-corruption and anti-doping rules and before the match spoke of overcoming alcohol and drug addiction to revive his Test career, which began 21 years ago.
"How good is it that three years ago, I couldn't get out of bed and now I am here doing what I love, and that's representing Zimbabwe?" Taylor said in an emotional television interview before the first day's play.
"I was in the dark depths of the abyss and trying to just get through this total and incomprehensible demoralisation of life. It was incredibly difficult."
He was the fifth Zimbabwe wicket to fall when a ball from Henry looked to stand up on him and he steered an easy catch to Mitchell Santner at extra cover.
Wicketkeeper Tafadzwa Tsiga made the only other significant contribution with an unbeaten 33.
Fast bowler Foulkes was one of three debutants for the Kiwis, whose captain Tom Latham failed a fitness test on a shoulder injury, with Santner deputising for a second successive match.
New Zealand had won last week's first Test, also at the Queens Sports Club, by nine wickets.
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