His partnership of 185 for the second wicket with Rilee Rossouw was the essential difference between the two side as New Zealand were unable to put together a stand of similar magnitude.
New Zealand were nevertheless in with a chance of winning most of the way through their innings until they lost two wickets in an over to the bowling of Vernon Philander.
Tom Latham (60 off 80 balls, 6 fours and a six) and Kane Williamson (47 off 69 balls, 4 fours and a six) gave New Zealand the platform they needed with a second wicket partnership of 194 in 21 overs but apart from the 71-run partnership for the sixth wicket between Jimmy Neesham and Colin Munro, they were unable to build on that effort.
Amla and Rossouw's partnership for the Proteas was their third major one during the current calendar year. They shared two partnerships of 247 against the West Indies at the Bidvest Wanderers Stadium and at SuperSport Park in January before today's effort of 185 which improved the previous second wicket record partnership against New Zealand of 172 achieved by Gary Kirsten and Jacques Kallis at Kimberley some 15 years ago.
Interestingly, Rossouw batted Nos. 2 and 4 for his two centuries against the West Indies and No. 3 today which underlines his versatility and adaptability.
Amla's century (124 off 126 balls, 13 fours and 3 sixes) was his 21st and thus equalled the South African ODI record held by Herschelle Gibbs.
New Zealand opened the bowling with Nathan McCullum, which was a surprise move, not because they used a spinner which is a regular practice in ODI cricket, but because Williamson had won the toss and opted to bowl first.
The batting conditions were, in fact, not easy in the first 10 to 20 overs. This was born out by Amla playing 33 dot balls in compiling his first 50 runs, this from a batsman whose one of many great strengths is his ability to keep dot balls to a minimum.
As always, Amla got his strike rate up to a run a ball by the end of his innings before being bowled by a low full toss from Milne that tailed in late as reverse swing became an effective weapon in the closing overs. Milne, in spite of bowling a few wides up front when he did not get his wrist behind the ball, was easily the pick of the Kiwi attack and deserved better figures than 2/51 from his 10 overs.
McClenaghan also picked up a key wicket in Rossouw (89 off 112 balls, 6 fours and 3 sixes) but tended to be erratic in his control of length.
The pleasing thing about Rossouw's innings was his ability to tough it out under difficult conditions and this was an important learning curve for his international career. Normally he likes to hit boundaries up front but this time he had to graft his way.
The New Zealand fielding was not up to its usual high standards with Rossouw (on 32) and Amla (74) offering chances that were not accepted. They nevertheless managed to restrict South Africa to 85/6 in the closing 10 overs.
Amla was the obvious choice as Momentum Man of the Match.
The second of the three matches will be played at Senwes Park, Potchefstroom, on Sunday (10h00 start).