Coming in with 69 still needed from 45 balls, Razzaq smashed 47 from 22 balls and with Muhammad Sami (17 from eight balls) turned the match as the home side sped to victory on 292 for seven in 48 overs.
New Zealand conceded 34 runs in the last two overs bowled by Michael Mason and Chris Cairns. Razzaq struck three fours and two sixes in all while tailender Sami hit two sixes.
New Zealand wicketkeeper Brendon McCullum dropped a miscued shot from Razzaq at 258 for seven and that proved decisive.
Captain Cairns could not supplement his blazing 84 from 51 balls earlier in the day that powered New Zealand towards a challenging 291 for five in 50 overs.
He proved to be the most expensive bowler for the visitors, going for 52 in six overs.
When New Zealand had batted Pakistan were clearly surprised by the spirit shown by a depleted side playing with six debutants in the absence of key players.
Mathew Sinclair (55) and new boy Hamish Marshall (also 55) laid the foundations with a third-wicket stand of 99.
In the Pakistan innings, the Kiwis appeared to have the match under control when Cairns trapped Inzamam-ul-Haq leg before for 49 in the 36th over.
But they had reckoned without Razzaq who earlier in the day had also taken two wickets.
The next match in the five-game series is in Lahore on Monday.
Scoreboard
New Zealand
C.Cumming c Imran Farhat b Shabbir Ahmed 25
R.Jones b Abdul Razzaq 16
M.Sinclair st Moin Khan b Shoaib Malik 55
H.Marshall lbw Shabbir Ahmed 55
C.Cairns not out 84
J.Oram c Misbah-ul-Haq b Abdul Razzaq 35
B.McCullum not out 0
Extras (lb-5 w-8 nb-8) 21
Total (for five wkts, 50 overs) 291
Did not bat: D.Vettori, M.Walker, K.Walmsley, M.Mason.
Fall of wickets: 1-49 2-57 3-156 4-178 5-268
Bowling: Muhammad Sami 10-0-67-0 (nb-3 w-5), Shabbir Ahmed 10-0-30-2 (nb-2 w-1), Abdul Razzaq 10-1-71-2 (nb-3), Danish Kaneria 10-0-76-0 (w-1), Shoaib Malik 10-0-42-1 (w-1).
Pakistan
Imran Farhat c McCallum b Mason 0
Yasir Hameed c Sinclair b Oram 52
Yousuf Youhana run out 42
Inzamam-ul-Haq lbw Cairns 49
Moin Khan c McCallum b Vettori 43
Shoaib Malik c Walker b Walmsley 9
Misbah-ul-Haq c Cumming c Oram 21
Abdul Razzaq not out 47
Muhammad Sami not out 17
Extras (lb-7 w-2 nb-3) 12
Total (for seven wickets, 48 overs) 292
Fall of wickets: 1-2 2-92 3-95 4-194 5-196 6-223 7-227
Bowling: Mason 9-0-61-1 (nb-3), Walmsley 10-0-64-1 (w-1), Cairns 6-0-52-1, Oram 8-0-33-2 (w-1), Vettori 10-0-50-1, Walker 5-0-25-0.
Result: Pakistan won by three wickets.