New Zealand chased down 149 in the 16th over to book a spot in the final agianst England.
South Africa made 148 for six with Hayley Jensen (2-24) and Amelia Kerr (2-28) the pick of the New Zealand bowlers.
Suzie Bates (62) and Sophie Devine (68 not out) then put on 130 for the opening partnership to set up the victory.
The White Ferns then had a quick turn around and played England, losing by seven wickets.
Batting first, New Zealand were bowled out in the 19th over for 129. Devine once again top scored with 52 - but only two others players made double figures. England's Anya Shrubsole took 3-16.
England were untroubled in the chase after losing an early wicket, reaching 130 for three in the 16th over. Sarah Taylor made 51 from 37 balls to lead the way.