The South Africans won 18-17 after the match went to an extra end.
"It was neck and neck, they had it and then we had it," said the experienced Piketh.
The South Africans were 14-17 down before they fought back to equalise on the final end.
"We were a little bit nervous and anxious, but we knew what we needed to do," said Botha.
Botha was also a member of the medal-winning fours team.
"It was extremely tense. Once that final bowl happened, the relief you feel, that's when the emotions come out," said Botha.
"They started catching up and we had to recompose ourselves."
In the final end England's Natalie Melmore missed on a drive with her team's last bowl. The South African duo had a bowl left but it was not needed as they won the final three shots of the match.
"We were hanging on by the skin of our teeth and we pulled it off," said Botha.
"We're so proud to have come back the way we did."
South Africa now have five gold medals in bowls at the event, two more than any country has managed before.