The left-handed opener held his ground even as wickets tumbled around him, before he was ninth out in the 44th over trying to force the pace Monday.
Fleming, who hit 11 boundaries, missed his 10th one-day century by 11 runs when he pulled Jacques Kallis to be caught on the fine-leg boundary by Shaun Pollock.
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 slow 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 celebrated his 31st birthday with 3-28 off seven overs. Left-arm spinner Robin Peterson picked uo 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).
Fleming and Nathan Astle put on 47 for the second wicket when South Africa hit back with three wickets in the space of 12 runs.
Astle (14) was bowled by Andrew Hall before Hamish Marshall fell in similar fashion to Andre Nel. Kallis had Peter Fulton caught behind by wicket-keeper Mark Boucher off his sixth delivery.
Peterson checked New Zealand further when he had Jacob Oram caught at short-leg and the took a smart return catch to dismiss McCullum.
Sri Lanka and Pakistan, who clash in Jaipur on Tuesday, are the other two teams in the group.
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.
Brief Score: New Zealnd 195 all out in 45.4 (S Fleming 89, Brendon McCullum 21; J Kallis 3 for 28, Peterson 2 for 34, S Pollock 1 for 18) vs South Africa