After losing all three of their matches on Saturday’s opening day, they went down 44-35 against hosts New Zealand and were left in a race to avoid the wooden spoon.
The South Africans bounced back, however, to secure a narrow 33-30 consolation victory over Malawi in their last round-robin fixture.
They avoided bottom spot in the playoff for fifth and sixth positions, bagging a 30-22 win over the Malawians.
New Zealand remained unbeaten throughout the five-a-side tournament, edging Australia 35-31 in the final to lift the title for the fifth time in six years.
England defeated Jamaica 31-30 to pocket the bronze medal.