The Black Caps total could have been 201-1 with three batsmen Latham, Neesham and Worker all retired by coach Mike Hesson to rotate the time in the middle.
The hosts in reply showed character with Wihal Lubbe (40 from 34 balls) leading the way but they couldn't keep with the required run rate of 10.1 per over and in the end finished 73 runs short on 128-5.
At the start of the day, Latham and Williamson set up a big score with an attacking opening stand of 85.
Latham, who is likely to join Martin Guptill in the opening pair for the upcoming ODI series, delivered at the top with six fours and a six.
Skipper Williamson at the other end was at his effortless best as he hit eight fours around the full wagon wheel of the Potch ground.
His innings came to an end when he was spectacularly caught by Lubbe at cover from the bowling of Drain Wyers in the 11th over.
When the Black Caps reached 123 in the 14th over, Latham was retired and Neesham made his way out to the middle for New Zealand for the first time in almost nine months.
Neesham was straight into his work and produced a powerful innings of shot making that included five fours and two sixes to continue the momentum.
He combined with Worker, who made his first start for the Black Caps for a 61 run partnership, and the all-rounder from the Devon Hotel Central Stags looked right at home in the dry conditions.
Worker made a telling cameo of 26 before he was retired to give Adam Milne (6*) some time at the crease.
Neesham also made way for Grant Elliott (4*) after he delivered exactly what Hesson would have wanted to see from him.
The powerful all-rounder (with 2 wickets for 22 runs from 3 overs) finished with the best bowling figures for the Black Caps while Worker (1-13), Ben Wheeler (1-14) and leg spinner Ish Sodhi (1-20) were also among the wickets.
The bowling effort was also a success for Milne (4 overs, 0-37), who returned for the Black Caps for the first time since being ruled out of the ICC Cricket World Cup with a heel injury.
The Black Caps will play a 35 over match against North West Cricket Club tomorrow at Potchefstroom in their final warm up game ahead of the first ODI against Zimbabwe in Harare on August 2.