He edged seamer Tim Southee at catchable height between wicketkeeper Luke Ronchi and first slip on seven. Neither moved for it.
Five runs later he top edged a hook off the same bowler and Dan Vettori at fine leg completely lost the ball. What should have been a regulation catch hit the ground 15m away from the unsighted fielder.
From then on, Amla was in charge, working the ball about the park and at times getting his runs in clumps.
His 100 took 127 balls, then he went on a tear, ripping off four boundaries in four Trent Boult deliveries.
Du Plessis hit an entertaining 67 off 73 balls and de Villiers a brisk 37.
However South Africa's lower order crumbled, losing their last six wickets for 25 to fall short of what should have been a routine 300-plus total.
On a pitch which played a touch quicker than it had in the opening game of the series last Tuesday, Southee, Trent Boult, McClenaghan and Corey Anderson finished with two wickets each, and Jimmy Neesham one each.
New Zealand were in trouble early when openers Martin Guptill and Neesham gone inside the ninth over with 29 on the board, and never recovered.
Captain de Villiers took his first ODI wickets while Dale Steyn, Vernon Philander and legspinner Imran Tahir all caused problems as New Zealand tumbled.
Only wicketkeeper Ronchi, top scoring for the second straight game, with 79, and McClenaghan with an unbeaten 34 stood up to the challenge.
The final game is in Hamilton on Monday.
Scoreboard
