Martin Guptill hit an unbeaten 91 as New Zealand chased down Zimbabwe's 8-159 in Auckland on Friday.
Guptill collected five fours and six sixes in his sixth consecutive international half century as the Black Caps won the first of two Twenty20 internationals by seven wickets.
Guptill, who scored 232 runs in the three one-day internationals, shared a match-winning partnership of 137 runs for the third wicket with Kane Williamson (48).
New Zealand reached the total off 16.5 overs, with Kyle Jarvis (2-25 from two overs) the only successful wicket taker for the tourists as Keegan Meth (0-13 from two) produced an economical shift.
After being set 160 for victory, New Zealand got off to a comfortable start before Rob Nicol was bowled by Jarvis for 12.
Kiwi hearts were firmly in their mouths when Jarvis had the prize wicket of captain Brendan McCullum for a golden duck as New Zealand stuttered to 2-15.
But that fear was soon replaced by jubilation as Kiwi opener Guptill found his rhythm to the delight of the crowd of just over 9,000 at Eden Park.
Guptill reached his half century from just 27 deliveries but did not slow down as he blasted a six with his next scoring shot.
The 100-run partnership for the third wicket was then achieved from 63 deliveries and left the hosts requiring 45 from just under a run-a-ball for victory.
New Zealand, however, refused to hang around as Guptill continued his hot scoring spree to finish unbeaten on 91 as a comfortable two saw the result formally ended by seven wickets with 19 balls remaining.
Earlier, Zimbabwe had finally displayed some of the batting talent that has been hinted at with Hamilton Masakadza blasting three boundaries and three sixes to top score with 53 off 36 balls.
Elton Chigumbura also cleared the fence four times and hit three boundaries as he scored 48 from 24 deliveries at the close of the innings.
Left-arm seamer Michael Bates, who bowled Zimbabwe captain Brendan Taylor in his first over, grabbed two wickets in the 20th over to finish with innings best figures of 3-31.
Zimbabwe's tour ends with the second Twenty20 international at Seddon Park in Hamilton on Tuesday.