Reaching the semi-finals is still a long shot; New Zealand must defeat unbeaten England next Saturday at The Oval and hope other results go their way.
England and the West Indies, who meet Wednesday (local time) lead the group with England on six points from three games, two more than New Zealand from four.
Izzy Sharp and Brooke Halliday pulled New Zealand out of 3-26 in a wretched powerplay with a partnership of 101 that wasn't broken until victory was only five runs away.
Sharp was the aggressor and out for a 43-ball 62, her career-best T20 score, and Halliday was unbeaten on 41 for New Zealand to reach 4-132 with 10 balls to spare.
"What a special knock from Sharp," New Zealand captain Melie Kerr said. "She has the potential to be one of New Zealand's best ever and the best in the world."
Scotland were eyeing a 150 total but were pulled back to 7-131 in the by the bowling of Sophie Devine, Nensi Patel, Bree Illing and Kerr.
Put in to bat in their first international against New Zealand, Scotland got a flying start from opener Darcey Carter, who had 36 runs in a powerplay of 45-0. Carter reached 50 off 37 balls, and two more dropped catches by New Zealand — their 12th and 13th in four games — had Scotland cruising.
Then Devine's first over of medium pace netted two wickets, Scotland were squeezed and Kerr returned in the 19th with a double wicket maiden to finish with 3-17. Carter was stranded on 72 not out.
New Zealand made the 132 target look towering when three down in the powerplay and Halliday survived the second ball she faced in the sixth over when her edge only grazed the fingertips of wicketkeeper Sarah Bryce.
Halliday didn't grab a boundary until the 14th, content to let Sharp lead. They accelerated after the 14th over by taking 12 off each of the next three overs.
The loss knocked Scotland out of last four contention.
In Tuesday's later group 2 match in Bristol Sri Lanka drew level with New Zealand after Chamari Athapaththu's brilliant century earned them an emphatic win over Ireland.
Ireland, who have lost all four matches, made 5-130, captain Gaby Lewis top-scoring with 59.
Sri Lanka knocked the runs off with nine wickets and 27 balls to spare. Athapaththu hit an unbeaten 106 in 61 balls.
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