Taibu, well supported by debutant Keith Dabengwa and Blessing Mahwire, rescued Zimbabwe from a perilous lunchtime score of 75 for 6 as the African side fought back to post 231. In reply, New Zealand reached 48 for 2.
Zimbabwe were hammered in the first Test and, with paceman Shane Bond on song, it seemed a repeat might be on the cards until Taibu led the recovery.
First the wicketkeeper-captain put on 49 for the seventh wicket with Dabengwa, who contributed a useful 17 before being bowled by Chris Martin.
That brought Mahwire to the crease and he accumulated 26 by tea, complementing Taibu's 66in a stand of 65, with the score moving on to 188 for seven.
When play resumed, the two continued to move the score along until Taibu departed for 76, mistiming a hook off Bond's bowling.
That partnership had added 90 runs for the eighth wicket, but Daniel Vettori soon removed Mahwire for 42, caught by Nathan Astle.
Vettori then claimed the final wicket as Christopher Mpofu was caught by James Marshall at short leg. But Bond was the hero for the Black Caps with 6 for 51.
New Zealand lost the wickets of James Marshall and Hamish Marshall before the close.Reuse content