Once Amla settled in, the result was never in doubt, his classy 92 off 107 balls guiding South Africa home with a whopping 70 balls to spare.
His strike rate is superior to all South Africa's leading batsmen, past and present, bar de Villiers and his average is a cracking 56.1.
His strokeplay was superb, his driving precise, his placement top class.
Back-to-back stands between Amla and Faf du Plessis, then Amla and JP Duminy banged nails into the New Zealand cause and by the time Amla departed to a beauty from legspinner Tarun Nethula the job was all but done.
But the game was lost much earlier in the day in a way McCullum found unacceptable. Certainly South Africa's bowling applied pressure, but the batsmen butchered a solid foundation.
"We had the middle ripped out of us. Losing eight for 60 is not acceptable. Ultimately we left our bowlers with nowhere near the score they needed to defend," McCullum said.
"Some of our options weren't great and the execution of those options even worse."
A shame, then, that it was McCullum's dismissal, 15 shy of a fifth ODI hundred, which put the skids under the New Zealand innings.
He and Martin Guptill had set the innings nicely with their 107-run second wicket stand.
Starting from the dismissal of Kane Williamson, in the first over of the five-over batting powerplay, New Zealand lost five for 23 from 33 balls.
McCullum, in his 200th ODI, the sixth New Zealander to the mark, needed to press on. His downfall came attempting to find the stands a third time, flicking Lonwabo Tsotsobe to deep square leg. His frustration was evident, and understandable.
It came at a time when, quite apart from having a big century for the taking, he was needed to anchor the innings through to the end. Instead Jesse Ryder, feet not moving, James Franklin, edging a lifter down on to his stumps, and Kyle Mills were gone in a jiffy and it was all uphill.
Man of the match Morne Morkel took his best ODI figures, five for 38. But Dale Steyn is the thoroughbred of the South African attack.
He was up to 145km/h in his first over and, used in short bursts, is warming up impressively for the tests series.
"I thought we played consistently well in all three disciplines," a delighted de Villiers said. "The boys stuck to their game plans and did exceptionally well. To restrict them to under 250 was unbelievable on that wicket."
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