New Zealand responded with a century stand from their openers but were lucky to escape with the win after losing frequent wicket near the end of their innings.
With the in-form Martin Guptill left out of the side, James Franklin took his place at the top of the order and after a slow start with Rob Nicol - the duo set up a platform by putting on 103 for the first wicket.
Nicol fell in the 11th over for 56 from 37 balls hitting eight boundaries including four sixes before he was caught in the deep by Keegan Meth as Elton Chigumbura struck with the first ball of his spell.
Franklin passed his previous best of 43 to bring up his maiden T20 half century in a well paced innings which included five sixes before a mix up with Brendon McCullum saw the Wellingtonian run out for 60 when Meth threw down the stumps from the boundary rope.
Colin de Grandhomme arrived at 142 for two in his first bat for New Zealand but could only manage eight runs before he played on to Chigumbura.
That brought the two McCullum brothers together and they seemed content to keep the run-rate at around 10-an-over and rely on big hitting at the end of the innings to secure victory.
Needing 27 from the last two overs, Brendon McCullum hit a six before sending the next ball straight to Malcolm Waller on the square-leg boundary off Kyle Jarvis for 38.
Nathan McCullum went the next ball to the other side of the field but produced the same result, caught on the boundary by Chigumbura for five leaving New Zealand 180 for five and needing 21 from nine to win. Williamson and debutant Andrew Ellis only needed seven deliveries.
Earlier Zimbabwe decided to bat first after winning the toss yet again and got off to a fine start, letting none of the five New Zealand bowlers used in the first seven overs off the hook.
The tourists added 76 in the opening seven overs for the first wicket before Ronnie Hira made the breakthrough as Stuart Matsikenyeri holed out to Tim Southee at deep mid off for 32 including three sixes.
Fellow opener Hamilton Masakadza continued the hard hitting and brought up his fourth Twenty20 half century in just 26 balls with his fourth six.
He batted through to the 14th over and reached 62 off 42 balls before he skied a high catch to Colin de Grandhomme off the bowling of Michael Bates leaving Zimbabwe 121 for 2.
Taylor continued the onslaught and put away frequent poor deliveries from the New Zealand bowlers who failed to find rhythm, possibly due to the 15 bowling changes made throughout the innings.
Taylor finished with his third Twenty20 half century, putting on 79 runs for the third wicket with Elton Chigumbura who added a handy 29 off 16.
All but one of New Zealand's eight bowlers went at more than eight-an-over.
- HERALD ONLINE