Captain Inzamam-ul-Haq (72) and Yousuf Youhana (88) quickly scored the 28 runs needed to round out an improbable win.
Rain, which twice delayed the start of play Tuesday, couldn't save New Zealand from an embarrassing match and series defeat, its first test loss in 10 matches.
New Zealand had seemed in a strong position when it took a 170-run first innings lead, dismissing Pakistan for 196 in reply to its first innings of 366.
It was still in charge of the match when it led by 245 with seven second-innings wickets in hands at the start of the fourth day.
But Pakistan fast bowler Shoaib Akhtar destroyed New Zealand's batting with an impeccable period of reverse-swing bowling Monday, rushing them out for 103 and leaving his team only 274 to win.
That win was a formality when Pakistan reached 246-3 by the end of the fourth day with its most experienced batsmen, Inzamam and Youhana, on top of the New Zealand attack.
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