Captain Brendan Taylor, with an unbeaten 75, led Zimbabwe to 200-2 batting first - its highest score in a Twenty20 - and New Zealand rode highs and lows before sneaking to victory from the fourth ball of the final over.
The win left New Zealand unbeaten in all forms of the game in the series against Zimbabwe. It won the one-off test by an innings and 301 runs, swept the three one-day internationals and took the opening Twenty20 by seven wickets.
"Zimbabwe played how we thought they would at some point on the tour," captain Brendon McCullum said. "They played well, put us under pressure and we didn't respond well which is something we'll have to look at. Now we move on to South Africa pretty pleased with where we're at."
New Zealand now faces South Africa in three tests, three one-day and three Twenty20 internationals. The first Twenty20 is at Wellington on Friday.
Zimbabwe turned in the most competitive performance of its tour in its final match, taking advantage of an outstanding start provided by Hamilton Masakadza and Stuart Matsikenyeri who put on 76 for the first wicket from 42 balls.
Masakadza reached a half century from 26 balls, the fastest by a Zimbabwe player in Twenty20s, and went on to make 62 from 42 balls in an innings which set up Zimbabwe for a substantial total. Matsikenyeri made 32 from 19 balls and the openers set the tone for the innings and the match, smashing seven sixes and five fours.
Masakadza hit the first six of the innings in the third over, planting a long hop from Kyle Mills onto the roof of the grandstand at Seddon Park. Matsikenyeri followed suit, hitting two sixes from the fourth over of the innings bowled by Michael Bates. The first, down the ground, struck the sight screen on the full.
In that mood, the openers guided Zimbabwe to 40 without loss after four overs and to 65 after six. Matsikenyeri was first out, in the seventh over, but Masakadza kept the runs flowing in partnership with Taylor, taking Zimbabwe to 98-1 after 10 overs.
He was out when Zimbabwe was 121-2 in the 14th over and Taylor then steered the innings with his unbeaten 75 - the second-highest total by a Zimbabwe batsman in Twenty20s. He reached his half century from 31 balls with four fours and three sixes and took Zimbabwe to 200 for the first time in its Twenty20 history from the last ball of the final over.
New Zealand promoted allrounder James Franklin to open the innings with Rob Nicol in the absence of Martin Guptill, who was rested after scoring half centuries in his five previous innings against the tourists.
Franklin looked out of form early on and Nicol set the pace of the innings, lifting New Zealand to 46 without loss after five overs. But Franklin hit successive sixes off Shingirai Masakadza in the eighth over to gain some confidence and went on to post a century partnership with Nicol from 58 balls.
New Zealand's scoring rate slowly lifted to match Zimbabwe's. It was 103 without loss after 10 overs and 148-2 after 15, needing 53 to win from 30 balls. Nicol made 56 from 37 balls and Franklin 60 from the same number of deliveries to give New Zealand a solid platform.
Brendon McCullum then made 38 from 24 balls to keep New Zealand on target. But Kyle Jarvis put Zimbabwe back in the match when he removed McCullum and his brother Nathan with successive deliveries in the 19th over, leaving New Zealand 187-5 and needing 14 to win off the last over.
Andrew Ellis, in his Twenty20 debut, took a single from the first ball and Kane Williamson then hit four, six and four to carry New Zealand to its winning total and to finish 20 not out from only five deliveries.
