However, having restricted the Kiwis to 6-110 in Dubai Pakistan collapsed from 1-19 to 56 all out to lose by 54 runs. New Zealand thus claimed second place in Australia's group and a semi-final spot for the first time since 2016.
India, effectively by dint of their opening match defeat to New Zealand, missed out, also for the first time since 2016.
Pakistan's 56 was the second lowest total in the competition's history, beaten only by the 46 Bangladesh managed against West Indies in 2018, and four lower than Pakistan's previous worst, against England in 2009.
They did have some excuse. Pakistan had the chance of qualifying themselves, but only if they chased down their target in less than 11 overs. On a difficult pitch that meant they were forced into extravagant shots that they too often failed to execute.
However, there was no excuse for the eight catches Pakistan put down in the field, allowing New Zealand to score far more than they should have done.
"We were good in the bowling but we need to improve our fielding and batting because we were not up to the mark, Pakistan captain Fatima Sana said. "Our senior players need to step up in these kind of matches."
Opener Muneeba Ali set the tone for Pakistan with early boundaries but the innings soon collapsed. (AP PHOTO)
"It hasn't sunk in yet," said New Zealand captain Sophie Devine.
"Results haven't gone our way leading into this tournament but what I am most proud of is we stuck with our processes and our belief. When we get it right we can beat any team so to do this at a World Cup is something I am incredibly proud of."
New Zealand opted to bat and began well with Suzie Bates (28) and Georgia Palmer (17) putting on 41 off 39 balls but Pakistan's spinners bowled with pace off and were hard to get away.
Nashra Sandhu took 3-18 and Omaima Sohail 1-14 off her four overs while Nida Dar had three catches dropped in the final over as she finished with 1-26.
A 38-run partnership between Devine (19) and Brooke Halliday (22) helped New Zealand post a defendable total which soon looked a challenging one.
Muneeba Ali scored 15 off 11 but had no support from the rest of the top order. Sana top-scored with 21 at No.5 but no one else reached double figures.
New Zealand held their catches, ran two batters out and secured a stumping with Amelia Kerr (3-14 off 2.4 overs) and Eden Carson (2-7 off three) the pick of the bowlers.
New Zealand will now play the winner of the tournament's last group match between England and West Indies on Tuesday (Wednesday 0100 AEST) with either one of those two or South Africa set to play Australia in the other semi-final.
with agencies
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