Parnell took three wickets in his last two overs as New Zealand crashed from 203 for five to 214 all out, the 20-year-old finishing with career-best figures of five for 57 in eight overs.
"Wayne has proven his skills and it was great to see him bounce back today," Smith said. "He has put the work in at training and, although he will have his ups and downs because he is young and will have to learn quickly, as a captain it's important to show faith."
Left-arm spinner Roelof van der Merwe, who took two for 35, also received praise as South Africa recovered from their heavy opening loss to Sri Lanka.
"Roelof is one of the most competitive players in our squad, he even gets worked up in schools games. He plays at 100 per cent and it's great to see his skills are at the same level as his competitiveness," Smith said.
AB de Villiers produced a top-class innings of 70 not out off 76 balls to steer South Africa home on a difficult pitch.
"I thought to get us home in the 42nd over was a good effort," Smith said. "We knew the pitch would be a touch slow and we'd have to work harder with the bat today. The nature of the pitch was such that to really attack the spinner was tough."
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