Set a challenging 145-run target Pakistan lost wickets at regular intervals with opener Ahmed Shehzad (33) and captain Shahid Afridi (28) the only ones who stayed long enough to raise any hopes of a win.
Pakistan won the first match -- also played in Dubai -- by seven wickets on Thursday.
This time their chase was chaotic as New Zealand bowled with precision and fast bowlers Jimmy Neesham finished with 3-25 and Kyle Mills 3-26.
Pakistan also lost Mohammad Hafeez (nine) and Haris Sohail (three) and were struggling at 24-3 before Shehzad added 40 for the fourth wicket with Saad Nasim who made 19.
Afridi hit two towering sixes off spinner Daniel Vettori but was caught behind off Neesham with 24 needed in the last two overs.
Mills wrapped up the innings with the wickets of Umar Gul (nought) and Sohail Tanvir (11) to give his team victory.
Shahid Afridi pointed the finger of blame at his side's batting.
"We lost three early wickets and then played more dot balls and that made the target difficult," said Afridi.
New Zealand were given a sound start of 49 for the first wicket by Williamson (32) and Devcich (21) but Hafeez (1-20) and Afridi (2-33) applied the brakes with three quick wickets.
Williamson hit three boundaries and a six in his 31-ball knock.
Ronchi hit two towering sixes in one Afridi over and one boundary during his 19-ball knock.
Paceman Gul, playing his first match since April due to knee problems, finished with 2-24 in his four overs.
The two teams now play a five-match one-day series, the first of which will be played in Dubai on Monday.
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