But Nicky Boje hit a two off the first ball of the final over from Shane Bond before, with all the fielders up to prevent a single, he skied the third delivery just out of the reach of a diving New Zealand captain, Stephen Fleming, for the winning run.
Both Kemp and Pollock survived chances before taking South Africa to their target of 250.
Fleming said New Zealand's 249 for eight was a "reasonable total" on a slow pitch against accurate bowling and lively fielding.
Craig McMillan top-scored with 66 and shared a fifth-wicket stand of 75 off 103 balls with Jacob Oram (35).
Fleming made a sparkling 45 off 48 balls with nine boundaries but the batsmen generally had difficulty in pushing the score along on a pitch that was unusually slow for Bloemfontein.
England vs Pakistan
England captain Michael Vaughan has insisted there will be no "Ashes let-down" for his side when they play Pakistan.
England's dramatic 2-1 home series defeat of Australia, the world's No. 1 ranked Test team, gave them the Ashes for the first time in 18 years and inspired a huge surge in cricket's popularity in the land of its birth.
But on the eve of England's departure for a three-Test and seven one-day match tour, Vaughan told reporters on Monday that his side would have to be at their best to win in Pakistan.
There are only five survivors from England's successful 1-0 win in a three-Test series on their last tour of Pakistan in 2000-2001 -- Vaughan, Matthew Hoggard, Ashley Giles, Marcus Trescothick and Andrew Flintoff -- in the current squad and Vaughan said his team would have to adapt quickly to the conditions.
"It's a big challenge and opportunity for the team to continue the progress we made in the summer," said Vaughan, a sight-screen pusher when England won five years ago in fading light in Karachi to clinch a dramatic Test and series win.
Pakistan pitches traditionally offer plenty of assistance to spin bowlers and although Bob Woolmer -- Pakistan coach and former England batsman -- recently contradicted his captain Inzamam-ul-Haq by saying he wanted to play the series on good, rather than turning, wickets, Vaughan was in no doubt about what sort of surfaces would confront his men.
"I would be very surprised if we go to Pakistan and it doesn't spin. But we have become decent players of spin over the last few years," Vaughan said.
England will be without injured reverse-swing specialist Simon Jones, one of their Ashes stars.
England play their first tour match in Rawalpindi, a three-day game, starting on Oct. 31 with the first Test at Multan commencing on Nov. 12.
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