The Black Caps, bowled out for 195 after being given first strike in the day-night international at the Brabourne stadium on Monday night, fought back to dismiss the powerful South Africans for 108.
New Zealand captain Stephen Fleming held his team's crumbling innings together with a defiant 89, inspiring his team-mates to make a spectacular comeback in the second session.
"It's always tough to sit and moan about a wicket when you've lost, but in terms of an international tournament I don't think the wicket was of a good standard," said Smith, South Africa's top scorer with 42.
"The pitch deteriorated as the day went along. Batting second was very, very difficult. All credit to Stephen. His knock held their innings together and without him, who knows, we might have been chasing 120-130.
"The pitch broke up, the ball turned a hell of a lot. I don't think the pitches are going to provide a 100 overs of good cricket."
Fleming, named man of the match, said he expected the the wicket to take turn.
"We went with what we saw, which was a very dry wicket, and as it turned out it got worse," he said.
"The pitches are a bit different this time around in India. As the tournament progress, it is going to be tough on the viewers and in this respect I can understand Graeme's complaints.
"But our job is to play on whatever pitches are given to us and play accordingly.
"We were aiming 220 to 230, which we thought was really competent on this pitch. Once we saw the ball stopping a bit off the wicket, we realized that we are in with a chance in this game," said Fleming.
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 surface.
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.
New Zealand seamer Kyle Mills, opening 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 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.
New Zealand next play Sri Lanka here on Friday. South Africa take on the Sri Lankans in Ahmedabad on October 24.
Meanwhile, veteran South African 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).