In the singles Madri le Roux eased to a 6-3, 6-2 win over Sandra Samir, and Chanel Simmonds was 6-1, 1-0 up before Mayar Sherif was forced to retire injured.
The result meant South Africa had an unassailable lead going into the doubles rubber.
Natalie Grandin and Natasha Fourouclas teamed up in the doubles, and ran out 7-5, 6-4 victors over the pair of Ola Abou Zekry and Mayar Sherif, sealing a comprehensive scoreline in the tie.
The win for the South Africans was a welcome change in fortune after losing to Bosnia and Herzegovina, and Georgia earlier in the week.
On Saturday, South Africa will face Montenegro in their relegation playoff tie.