The match was marred by pro-Palestinian demonstrations after South African Sports Minister Thulas Nxesi boycotted the event due to Israeli government policies.
On court Israel's task was made easier by the absence of South Africa's world No. 11 Kevin Anderson. Israel's Idan Leshem (253) lost the opening rubber to Lloyd Harris (290) but Dudi Sela (97) drew Israel level with victory over Nicolaas Scholtz (328)
In the doubles, Sela and Jonathan Erlich lost 7-5, 4-6, 4-6 to Raven Klaasen and Ruan Roelofse.
The new abbreviated format in which Davis Cup matches are played over two days and the best-of-three rather than five sets, meant Sela had to come straight back on court. Looking tired, he nevertheless beat Harris 7-6, 6-1. Leshem then stepped up to beat Scholtz 6-3, 7-5.
Israel captain Harel Levy said: "Credit to the players for a great performance under difficult conditions. Dudi had to play eight sets in less than 24 hours and that was a big ask – but hats off to him for coming back on court and beating Harris the way he did.”
Israel’s reward for the victory is a trip to the Czech Republic in April.