Their cause was aided by three dropped catches, and then by a rollicking late run spree which added 60 runs in five overs at Mount Maunganui.
Fakhar scored 46 off 36 deliveries after Pakistan won the toss and made first use of a batsman-friendly track.
With the series tied 1-1, a win for Pakistan would not only give them the series but also propel them over New Zealand to number one in the world T20 rankings.
At the halfway stage, Pakistan were 72 for two with opener Fakhar on 32 off 24 deliveries.
He added a further 14 runs before being given out in a debatable decision when Tom Bruce took a catch at ground level.
Television replays were inconclusive on whether the ball touched the grass and after lengthy deliberations the third umpire ruled in favour of the onfield decision.
All his runs came in one over from Ish Sodhi before the New Zealand spinner took Umar's wicket with his final ball.
Haris Sohail made 20 off 12 balls and Aamer Yamin, replacing the injured Hasan Ali, faced six balls for 15.
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