Among the keys to the win was the job defensive duo of captain Casey Kopua and Leana de Bruin on Fowler-Reid, who prefers to shoot from close range. New Zealand had success by forcing her further out.
Jamaica didn't mess about at quarter time, swapping both defenders at the first break, bringing on the tall Romelda Aiken and former Tactix defender Casey Evering.
Aiken, with her long reach immediately caused problems, particularly for Halpenny, as Jamaica went ahead for the first time at 21-20, and they held the advantage 24-23 at halftime.
Fowler-Reid, after missing her second shot, got into her work and was becoming a near unstoppable force for a time.
Jamaica were encouraged by the presence of Usain Bolt, who arrived shortly after the start. He was the centre of attention in the arena, particularly at halftime when the photographers had a field day.
The Silver Ferns swapped Brown and Halpenny's roles at three-quarter time and although Halpenny looked jittery at times, New Zealand were up 35-33 going into the last 15 minutes.
The Silver Ferns shot at 72 percent success rate to Jamaica's 89. Brown nailed 31 of 40 shots, Halpenny only 16 of 29, while Fowler-Reid missed just four shots of 39.
Earlier Australia confirmed top spot in their group with a 64-40 win over South Africa.