Having got to 32 from the first five overs, Anton Devcich, Dean Brownlie and Williamson departed in the space of nine balls, Brownlie distinctly unlucky to go lbw to a poor umpiring decision.
Ross Taylor struggled but Latham, sweeping hard, got to 26 off 22 balls, having put on 38 with the increasingly important Ronchi.
The wicketkeeper's second decent contribution in two days ended at 31 off 19 balls, caught at deep mid wicket and when Dan Vettori stepped well across to the offside in a trademark move he exposed his stumps and classy veteran Umar Gul struck them. With that, New Zealand had suffered their second mini collapse, three for 11 in the space of 12 balls.
New Zealand managed 27 runs off the last three overs. Gul, back after an injury layoff, took two for 24 and Afridi two for 33.
Pakistan were in difficulties early as part time left arm spinner Devcich nipped out Sarfraz Ahmed and Mohammed Hafeez inside his first nine deliveries.
From 24 for three it was uphill for the hosts, but a 40-run stand between Ahmed Shezhad and Saad Nasim had them back in the contest.
With five overs left, Pakistan were 91 for five, two runs and one wicket behind New Zealand at the same point.
Big hitting captain Afridi slammed 28 off 10 balls to the crowd's unbridled delight. However Pakistan's hopes effectively died when he was given caught behind, trying to hook a Jimmy Neesham bouncer.
New Zealand had given themselves enough cushion to finish the job, senior seamer Kyle Mills taking the final wicket to give him three for 26 from 3.5 overs.
Neesham took three for 25 off his three overs while Devcich followed his run-a-ball 21 with two for 16 from four very handy overs.
"It was nice to have a little bit more responsibility today," said Neesham. "In the last game I didn't bowl until the last over which was a wee bit disappointing I suppose but with Corey sitting today's game out there was always going to be a bit more responsibility on my shoulders."
"Anton bowled extremely well for us today and obviously his batting at the top of the order is coming along as well, so hopefully we'll see a lot more of him in Black Caps colours."
The five-game ODI series starts on the same ground on Tuesday morning (NZT).
