Spinner Ish Sodhi in action during the second T20I — AFP
Fakhar responded by belting three sixes off Santner's first over, bringing up his maiden T20 half century soon after off 26 balls.
Rance finally broke through in the 9th over, deceiving Ahmed with a slower ball that carried straight to Colin de Grandhomme on the boundary.
De Grandhomme pressed home the advantage in the next over when he coaxed an edge to dismiss Fakhar and threaten to steal Pakistan's momentum.
But Sarfraz and Babar kept the scoreboard ticking over, taking Pakistan to 137 for two with five overs remaining.
Sarfraz in particular displayed a confidence that had so far eluded him on tour and also had a dash of luck when Mitchell Santner dropped him on 35.
He proceeded to send a Wheeler delivery into the stands but was out on 41 trying for a repeat with the next ball.
Babar brought up his 50 and took the team past 200 with a four off the final ball of the innings. Ben Wheeler was New Zealand's best bowler with two for 36.
“It looks a good batting pitch so hopefully we can come up with a good score then defend it,” captain Sarfraz Ahmed said after winning the toss.
“I've just told the boys 'play your natural game, don't worry about the result, we have nothing to lose'.”
Pakistan recalled opening batsman Ahmed Shehzad in a bid to make a strong start as they chase their first win on tour against the Black Caps.
New Zealand skipper Kane Williamson returns for the hosts after missing the first match with a thigh strain. Trent Boult is also back alongside rookie paceman Ben Wheeler, while Tim Southee is rested.
The three-match series will finish in Tauranga on Sunday.
New Zealand: Martin Guptill, Colin Munro, Kane Williamson (capt), Tom Bruce, Glenn Phillips, Colin de Grandhomme, Mitchell Santner, Ben Wheeler, Ish Sodhi, Seth Rance, Trent Boult.
Pakistan: Fakhar Zaman, Ahmed Shehzad, Babar Azam, Sarfraz Ahmed, Umar Amin, Haris Sohail, Shadab Khan, Faheem Ashraf, Hasan Ali, Mohammad Amir, Rumman Raees.
Series: New Zealand lead the three-match series 1-0 Umpires: Shaun Haig (NZL), Chris Brown (NZL) TV Umpire: Wayne Knights (NZL) Match referee: Richie Richardson (WIS)