The hosts failed to shine against a side who had defeated Cameroon 3-2 on aggregate to reach the finals.
Luis Platini had the best chance of the first half of the Group A encounter for the Blue Sharks, who then saw Helton denied after the break by South Africa goalkeeper Itumeleng Khune.
Ryan Mendes had the first shot of the game but the Cape Verde striker fired wide from 20 yards.
Cape Verde goalkeeper Josimar Vozinha then made hard work of a free-kick from Siphiwe Tshabalala.
Platini shot wide when well placed as Cape Verde continued to look for the opening, while Ramos Nhuck fired a free-kick over after Kagisho Dikgacoi had fouled Platini.
Elvis Babanco saw his shot go wide as Cape Verde continued to try their luck, Platini also missing and Dikgacoi off target as chances came at each end.
Cape Verde were awarded a free-kick but Babanco shot straight at keeper Khune, Mendes then shooting wide from close range.
South Africa's Lerato Chabangu came on for Dikgacoi at half-time and was in the action inside five minutes but shot over from close range.
Cape Verde went close with 18 minutes to go as Helton headed Babanco's cross towards goal but Khune got down low to his left to scramble the ball round the post.
In a rare South Africa attack Thulani Serero failed to control the ball with five minutes to go after being put in behind the Cape Verde defence.
South Africa's best chance came in injury time from a Lerato Chabangu corner to the near post - but captain Bongani Khumalo put his free header well over.