At 53 for two after 8.3 overs South Africa were right in the game, until Benade's rapid innings of 24 came to an end. Her 16 ball tenure concluded when she was caught by Morna Nielsen off the bowling of Nicola Browne.
Hodgkinson remained in the middle, but fell for 31 in the 12th over, effectively ending South Africa's chances.
A collapse followed her dismissal, as the White Ferns began to strike regularly. It soon became obvious that the result was never in doubt, despite a valiant effort from number eight Dane van Niekerk who ended the innings unbeaten on 34.
Browne was formidable with the ball and finished with figures of three for 13, while Sophie Devine and Bermingham picked up two apiece.
Earlier the White Ferns had overcome a slow start to post a very competitive total of 151 for five.
Openers Suzie Bates (14) and Amy Satterthwaite (2) were out early, leaving New Zealand 24 for two. The two new batsmen Devine and Frances Mackay initially struggled to get on top of the South African bowling attack, but soon found their rhythm and punished them with a 94-run stand for the third wicket.
Devine struck three sixes and five fours in her 59 from 46, while Frances Mackay fell just one run short of her half century with 49 from 40.
Both Sara McGlashan (9) and Browne (9*) finished off the innings with quick cameos, as the White Ferns surpassed the 150 mark.
Benade was the best of the South African bowlers, picking up figures of two for 15 from four overs.
The White Ferns will next play host nation Sri Lanka on Sunday, where a win will book them a ticket in the semi-finals.