The Blitzboks beat Samoa and Kenya before going down to New Zealand 24-19 on the opening day of the Glasgow Sevens.
The loss to the Kiwis in a rematch of last year's Commonwealth Games final means they will now face the unenviable task of overcoming the Fijians in tomorrow's Cup quarter-final.
They had earlier overturned a half-time deficit to see off a spirited Kenyan side 22-5 after edging Samoa 19-12 in their opening match. Those two victories helped South Africa secure their Olympic berth at Rio 2016.
However, they were unable to stay with the Kiwis in the pool decider, trailing from start to finish. Neil Powell's side suffered an early blow as Cecil Afrika limped off in the opening minutes after suffering a knock to his knee.
The loss of the playmaker was compounded further as Seabelo Senatla saw yellow shortly thereafter and New Zealand took full advantage to run in two tries and open up a 12-0 lead at the break.
A Senatla try early in the second half got the Blitzboks back into the match but the Kiwis hit back with a try from Tim Mikkelson, who injured himself in the process of scoring.
A moment of individual brilliance from Rosco Speckman briefly raised hopes of a Bok comeback, but that was quickly extinguished by another Kiwi try from Ambrose Curtis.
The Blitzboks would have the last say as Stephan Dippenaar crossed for a consolation try, but the New Zealanders had done enough to avoid a meeting with Fiji in the quarter-finals.
Sunday's Cup quarter-finals (to start 12:58pm SA time):
Australia vs USA
Fiji vs South Africa
Canada vs England
New Zealand vs Scotland
Photo: Mark Metcalfe/Getty Images
