Sri Lanka and Zimbabwe failed to progress to the Super League stage.
Four sides confirmed their berths in the Super League quarter-finals, which will be played in Townsville, Queensland on August 19 and 20.
In Thursday's match against Pakistan, the Kiwis won the toss and elected to bat, piling up a total of 152 runs in 50 overs at the loss of eight wickets.
Henry Walsh was the top scorer with 33 runs followed by Robert O Donnell (29), Joe Carter (21) and Will Young (18).
For the green-shirts, Zia ul Haq, Ehsan Adil and Mohammad Nawaz shared two wickets each conceding 27, 21 and 32 runs, respectively.
In reply, Pakistan reached the given target with ease in 31.2 overs, losing just five wickets.
Imam ul Haq was the pick of the batsmen hitting 40 runs including two 4s, while Saad Ali made 32 runs smashing four 4s while Mohammad Nawaz and Salman Afridi remained unbeaten at 23 and 18 runs, respectively.
For New Zealand, Theo van Woerkom bagged two wickets giving away 43 runs while Matthew Quinn and Sean Davey shared one wicket each for 22 and 29 runs, respectively.
Mohammad Nawaz was declared Player of the Match.
With this win Pakistan also tops its Group-B table with six points, New Zealand stands at second spot with four points followed by Afghanistan with two points.
Commenting on the team’s victory, Pakistan captain Babar Azam said he was confident his team would do well and was very pleased with the way the players have worked together as a unit.
"We have enjoyed our cricket so far and now we are into the quarter-finals," he said.
Meahwhile India outplayed Papua New Guinea (PNG) by 107 runs to book a date with traditional rival Pakistan.
Group standings
In Group A, England defeated Nepal by 126 runs to set-up a quarter-final meeting with South Africa, who had qualified for the last eight stage on Wednesday.
New Zealand's defeat to Pakistan meant it finished second in Group B and will play its quarter-final against the West Indies on Monday. West Indies topped Group C after defeating Zimbabwe by six wickets.
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This Zia ul Haq guy should change his name.