Amla (124) and Rilee Rossouw (89) shared a second wicket partnership of 185 as South Africa scored 304 for seven after being sent in to bat.
Amla had gone ten international innings without a fifty since making 159 against Ireland in a World Cup match in Canberra on March 3. In seven of those innings he failed to reach 20.
But much of Amla's customary fluency returned as he posted a half-century off 54 balls and his 21st one-day international hundred off 109 deliveries.
The left-handed Rossouw struggled to find his timing on a slow pitch, scoring only two runs off the first 17 balls he faced.
Also Read
He laboured to his fifty off 81 balls but picked up his scoring rate to finish with 89 off 112 balls. Rossouw also benefitted from a missed chance, dropped by Milne on the midwicket boundary off Grant Elliott when he had 32.
But only four of the New Zealand team and seven of the South Africans from the Auckland encounter lined up for Wednesday's game. Injuries, retirement and players being given time off accounted for most of the changes.
New Zealand opening batsman Martin Guptill fell awkwardly in trying to catch David Miller in the deep in the 48th over and left the field clutching his left wrist.