Down 2-0 in the series, the Ferns clinched the dead rubber match by six runs vial the Duckworth Lewis system.
Winning the toss, New Zealand sent Pakistan into bat and at 64/1, looked set for more misery before three quick wickets started a slide for the visitors.
Amelia Kerr snagged 3/11 off her four overs while Eden Carson bagged two scalps as Pakistan could muster just 137/5 off 20 overs.
Bernadine Bezuidenhout was dismissed early in the chase for just four when Suzie Bates was joined at the crease by skipper Kerr.
The pair plundered 63 when Kerr held out to Nashra Sandhu for 35.
Bates powered on to her half century off 42 balls while Maddy Green finished unbeaten on six.
As the clouds darkened the equation was made clear for the Ferns and the hosts ensured they were six ahead when the rain fell.
Bates said it was a very much needed consolation win and she felt extra pressure to perform after a couple of lean innings.
"You get a bit sick of not scoring runs and batting the way you know you so I dig deep every game to try and produce that but I think today it was even more important."
"It was massive for us to step up today, we were really disappointed with how we performed as senior players as well. So it was important that we got the job done."
Bates lauded teammate Kerr on her debut as captain.
"I thought she was outstanding, the way she managed the bowlers and how she bowled as well, it set up the game."
The veteran said she relished batting on the picturesque Queenstown ground.
"It's hard not to enjoy betting on that wicket, and we've talked as a group about being aggressive in the power play with both bat and ball and I don't think I've led from the front in there. So today I just made sure that as a senior player that I played in that nature and sometimes it comes off and sometimes it doesn't."
"This team is moving forward. The results are getting frustrating, but Pakistan were just too good for us in those two games so nice to have some momentum going into the one dayers."
Pakistan won the first two games in Dunedin by seven wickets and ten runs.
The ODI series gets underway on Tuesday.