With eight points from five matches, the Proteas can now not be caught by the White Ferns, who would still trail them on number of wins, even if they do win their final two group stage matches.
As a result, the Proteas join Australia in being assured a top four finish, although there is plenty yet to be decided in terms of seedings.
With this washout, New Zealand's next match against India is shaping up to be a winner-takes-all clash in Mumbai.
They chose to bowl in this one after winning the toss, with Lea Tahuhu breaking an opening partnership of 30 when she trapped Omaima Sohail leg before for three.
Muneeba Ali then departed to a brilliant Suzie Bates catch for 22 before Tahuhu (2/20) got her second as she removed Sidra Amin.
A first rain delay followed that dismissal, and after the resumption, Eden Carson and Amelia Kerr grabbed a wicket apiece to leave Pakistan in big trouble on 92-5 from 25 overs.
However, the rain returned and this time, the players did not come back out, with the game eventually abandoned and the points shared.
New Zealand skipper Sophie Devine said: "We had a little bit of hope seeing the South Africa game the other day and that they were off the field for five hours and came back.
"We just needed the rain to hold off, but it didn't happen today. But the situation is very clear, we have to win both games, starting with India in Mumbai.
"We head back to India tomorrow and look forward to the challenges."
Pakistan captain Fatima Sana added: "I think we got a good start but we lost a few wickets. But we had a good chance if we could have reached 180. We had a good belief in our bowling side.
"We will try to win the next two matches and try to end our tournament on a high note."
Pakistan debutant Razaullah, batting at number 9, smashed a record-equalling nine sixes to keep his team in the third Test against England at Edgbaston, with home needing a target of 130 to win.
Anneke Bosch smashed a career-best 83 as the Proteas Women opened their five-match T20I series against Zimbabwe with a convincing six-wicket victory in Bulawayo.
New Zealand white-ball captain Mitchell Santner has declined a lucrative offer from Australian Big Bash League side Adeliade Strikers to remain in contention for Test selection.
England moved firmly towards a 3-0 series sweep after a dominant second day of the third Test against Pakistan at Edgbaston on Thursday, with Ollie Robinson again proving the difference with both bat and ball.
