Veteran Jose Statham, playing a record 25th Davis Cup tie, downed Muhammad Abid 6-0, 6-1, 6-4 to give the Kiwis a perfect start.
Tournament debutant Finn Tearney was even more emphatic, crushing Samir Iftikar 6-2, 6-0, 6-0 to leave Pakistan on the brink in the best-of-five tie.
The winner will remain in Asia/Oceania Group I, with the loser relegated to Group II.
Pakistan are without their number one player Aisam ul Haq Qureshi, who pulled out because he was still angry about the last time the two teams met in Myanmar in 2013.
That tie was officially a “home” fixture for Pakistan — which has not hosted Davis Cup matches since 2005 due to security concerns.
But the grass court was deemed unplayable and the match referee awarded the tie to New Zealand, even though Pakistan were winning at the time.