Set a target of 272, Pakistan were all out for 256 with one over remaining. It is only the third time Pakistan have been on the wrong end of a 5-0 ODI clean sweep after they succumbed by the same margin to Australia in 2010 and the West Indies in 1988.
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New Zealand's innings was bolstered by a fine century from Martin Guptill that preceded a late collapse by the Black Caps.
The target should have been achievable, given the short boundaries at the Basin Reserve, but speedster Matt Henry ensured Pakistan made a disastrous start.
Called up to give Trent Boult a break, Henry made the most of his opportunity to take three wickets in three overs and skittle the tourists' top order.
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Pakistan slumped to 57 for five before Haris Sohail and Shadab Khan combined for a 105-run partnership that steadied the innings.
It ended when Sohail tried to loft the ball over the fence but misread spinner Mitchell Santner's slower delivery and instead offered Henry a straightforward catch.
His departure on 63, with Shadab following soon after on 54 seemingly ended Pakistan's faint hopes of victory.
But the tail wagged as Faheem Ashraf (23), Aamer Yamin (32) and Mohammad Nawaz (23) all made late cameos that left the tourists on nine for 249 and needing 23 off the final two overs.
The lack of wickets ultimately proved costly when Rumman Raees was dismissed with six balls remaining.
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