Sonny Bill Williams was solid on defence and got away three offloads but again New Zealand lacked the pace, guile and personnel to exploit a strong South African defensive wall.
Captain Liam Messam was sinbinned at the fulltime whistle after being penalised for holding on just metres from the South African line.
Coach Gordon Tietjens will be anxiously awaiting the return of his Super Rugby stars, the Ioane brothers and Ardie Savea, not to mention Tim Mikkelson, and DJ Forbes.
New Zealand will now play Australia in the Plate semifinals at 7.44pm NZT. Australia appeared to have their quarter-final in the bag but conceded two late tries to lose 19-14 to Fiji.
New Zealand will now slip back to third on the World Series standings with just two events to come next month in Paris and London.
South Africa 12 (Seabelo Senatla, Kyle Brown tries; Justin Geduld con)
New Zealand 7 (Kurt Baker try; Gillies Kaka con) HT: 12-7