The hosts had to overcome early losses on Friday, not least that of opener Nicol for a duck, to post 248, thanks largely to Martin Guptill's 70.
It was a target Zimbabwe always looked unlikely to chase down as their top three went for just 10 between them. Kyle Mills led the hosts' attack in a haul of three for 26, and Nicol took four for 19 as the tourists were bowled out for 158.
Stuart Matsikenyeri was trapped leg before by Mills with just three runs on the board before opening partner Hamilton Masakadza was run out by Andrew Ellis while on seven.
Mills then removed Regis Chakabva as Nicol took the catch and already Zimbabwe looked on the brink of defeat.
Some resistance was provided by the captain Brendan Taylor as he produced a 68-ball 58 featuring eight fours and a six, but he found little in the way of support before being caught by Ellis off Nicol. Tailender Ray Price managed 26 but ran out of partners, with Nicol taking another two scalps as well as his two catches.
The Black Caps had the biggest Test victory in their history after thrashing Zimbabwe by an innings and 301 runs in the one-off match in Napier last week, bowling out the African tourists twice in a day en route to an impressive victory.
But they provided a response yesterday as they bowled New Zealand out for 248, having made early inroads and frustrated the hosts' middle order.
Put in to bat by Taylor, New Zealand's innings got off to the worst possible start as Zimbabwe struck in the first over.
The Kiwis tried to steady themselves and Guptill (70) underpinned the resistance, Kane Williamson adding 35 in a partnership of 88 for the third wicket.