New Zealand, bowled out for 195 after being given first strike in the day-night international, fought back to dismiss the powerful Proteas for 108 in the most absorbing match of the tournament so far.
Man-of-the-match Fleming held New Zealand's crumbling innings together with a defiant 89, inspiring his team-mates to make a spectacular comeback in the second session on a dusty wicket at the Brabourne stadium Monday.
Seamer Kyle Mills, who opened the bowling in the absence of injured pace spearhead Shane Bond, grabbed three wickets with his first 19 deliveries to reduce South Africa to 25-3 by the eighth over.
The lanky Jacob Oram then ripped through the middle-order as the Proteas plunged to 71-6, 42 of those runs coming from captain Graeme Smith.
Off-spinner Jeetan Patel provided the finishing touches with 3-11 from 3.1 overs as New Zealand made a perfect start in group B that also includes Pakistan and Sri Lanka.
Left-handed Fleming, who opened the innings, remained rock-solid even as wickets tumbled around him, before he was ninth out in the 44th over close to his 10th one-day century.
Brendon McCullum was the next highest scorer with 21 as New Zealand, playing their first one-dayer since March, struggled to come to grips with the dry wicket that restricted stroke-making.
Fleming, who kept himself busy in the off-season leading Nottinghamshire in English county cricket, defied the South Africans for three hours under the sweltering heat and humidity.
South African all-rounder Jacques Kallis marked his 31st birthday with 3-28 off seven overs. Left-arm spinner Robin Peterson picked up 2-34.
Veteran seamer Shaun Pollock became the fifth bowler to claim 350 one-day wickets when he bowled Lou Vincent for 17 to end an opening stand of 27.
Pollock, 33, joined the rare club led by Pakistani Wasim Akram (502 wickets) and followed by Muttiah Muralitharan of Sri Lanka (419), Waqar Younis of Pakistan (416) and Sri Lankan Chaminda Vaas (358).
When South Africa batted, Mills struck with the fifth delivery of the innings when he trapped Boeta Dippenaar leg-before.
Mills clean bowled Herschelle Gibbs in his second over and took a splendid one-handed return catch in his fourth to remove Kallis.
Oram, who took over after Mills completed his opening spell of six overs, was smashed for two boundaries by Smith in his first over.
But the seamer hit back to have Mark Boucher caught behind for eight, forced the well-settled Smith to spoon a catch to mid-on and then removed Pollock to a catch in the deep.
New Zealand next play Sri Lanka here on Friday. South Africa take on the Sri Lankans in Ahmedabad on October 24.
Meanwhile, Pakistani umpire Asad Rauf returned home from India following the death of his mother. Rauf, who was due to be the television umpire on Monday, was replaced by Rudi Koertzen of South Africa.
Rauf is unlikely to return for the rest of the tournament which ends on Nov 5.