"It was a little bit closer than we would have liked," captain Brendon McCullum admitted.
"I think we were trying a little bit hard in the field to be honest. It wasn't our most clinical performance and we have to work on it in the coming days because we've got to be at the top of our game for the series (against South Africa) around the corner."
Williamson's hand he rated "outstanding" and thought the run chase was "pretty well-timed".
New Zealand's target was 10 an over, and Rob Nicol and James Franklin, promoted in Martin Guptill's absence, rattled up 103 in 10 overs.
Nicol led the way, man-of-the-match Franklin getting his sights first, and at one point they slapped six sixes in the space of 12 deliveries.
But Franklin's departure, run out by a terrific direct hit from Keegan Meth at deep square leg after a bruising 37-ball 60, gave the plot a twist before Williamson's bravura at the death.
This appeals as Zimbabwe's best form of the game. The five-day version is a stretch right now, given their inexperience, but this suits the idea of freeing them up to enjoy themselves.
Openers Hamilton Masakadza and Stuart Matsikenyeri let fly, racing past 50 inside five overs. It laid the platform, and set the tone, and Brendan Taylor and Elton Chigumbura made sure the groundwork was not wasted.
Both the first and third-wicket stands of 76 - from just seven overs - and 79 off 41 balls are Zimbabwe T20 records, and this was their first time reaching 200. Taylor was all class in his unbeaten 75 off 43 balls, while Chigumbura's 29 off 16 was just the ticket.
But too much of the bowling, frankly, was rubbish. Only they know if they were mentally switched on, but at times it didn't look much like it.
There was an inability to hit the blockhole often enough and too many free hits off full tosses were served up and not enough variety.
At a time New Zealand wanted to maintain their momentum ahead of the opening game against South Africa on Friday night, the bowlers forgot the script. It almost cost them dearly.