The win allowed Pakistan to finally break their losing streak of twelve games against the New Zealanders.
A six-wicket victory with 57 balls to spare has seen Pakistan level the series at 1-1 ahead of Monday morning's decider, and they were remarkably untroubled in doing so.
In his second spell, Shaheen yorked Tom Latham for one while Hafeez bowled George Worker for 28 to leave New Zealand struggling at 73-4. Ross Taylor has been the standout batsman for the Black Caps so far as he scored a match-winning century in the first game. New Zealand were 35-1 after 6.5 overs when the umpires signalled for a stoppage in play after light rain turned into heavy showers.
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Zaman scored his second successive half century before he holed out in the deep while attempting a big shot off Colin de Grandhomme. Azam was the top-scorer with 92 off 100 deliveries while opener Zaman got out for 65 earlier in the innings.
Opening batsman Imam-ul-Haq, who was struck on the helmet and retired hurt during the second ODI against New Zealand on Friday, will likely open the innings with Azhar Ali, with Mohammad Hafeez another option.
Pakistan lost four wickets in the last two overs and may regret scoring only 38 runs in the last five.
Going by the experience of the conditions, Pakistan holds the advantage in the last game before the Test series starts.
The pulling out of Kane Williamson, at the eleventh hour, left New Zealand, without its captain and gave the opposition, a huge advantage, before even the coin had been tossed.