Pakistan set a 129-run target for New Zealand in the fifth and last match of the five-match series on Wednesday in Wellington.
New Zealand captain Michael Bracewell decided to bowl first after wining the toss.
The visitors got off to an unwanted start as they lost hard-hitting opener Hasan Nawaz (0) in the second over with just five runs on the board.
Following the early hiccup, Omair Bin Yousuf joined Mohammad Haris in the middle for a brief 18-run stand, which was followed by their back-to-back dismissals.
Haris scored 11 off 17 deliveries with the help of two boundaries, while Yousuf made seven.
The green shirts then lost two more wickets in quick succession as Usman Khan (seven) and Abdul Samad (four) perished cheaply.
Their dismissals had reduced Pakistan to 52/5 in 10.2 overs until skipper Agha and experienced all-rounder Shadab recorded an anchoring partnership.
The duo added an important 54 runs for the sixth wicket until Shadab was removed by James Neesham on the first delivery of the 17th over.
The all-rounder scored 28 off 20 deliveries with the help of five boundaries.
Neesham inflicted another blow on the visitors as he sent Jahandad Khan back in the same over as Pakistan slipped further to 108/7 in 16.4 overs.
Agha also fell victim to Neesham in the penultimate over and walked back after top-scoring for Pakistan with a 39-ball 51, comprised of six fours and a six.
Neesham was the standout bowler for New Zealand, taking five wickets for just 22 runs in his four overs, followed by Duffy with two, while Ish Sodhi and Ben Sears chipped in with one scalp apiece.
