The tourists had appeared to be heading for defeat when trailing 20-9 early on in the second-half, but they struck back in fierce fashion as they notched up 17 points in eight minutes through a Morne Steyn penalty and converted tries from replacement Willem Alberts, on his first cap, and captain Victor Matfield to eventually claim the win.
For Wales it was the same old story, despite two tries on his debut from 18-year-old Scarlets wing George North, as they lost out in another nip-and-tuck encounter. South Africa's victory was the world champions' 12th in a row over Wales and their 23rd win in 25 Tests against them dating back 104 years.
But, despite this, Botha insists the Millennium Stadium contest was as tough as they come, especially during a first-half where Wales outshone their opponents in every facet of the game.
He said: "With all the guys injured at home and all the new players coming in, the character we showed was No 1. We came in at half-time with a setback on the scoreboard, but we stuck to our game plan and it came through for us.
"But it was definitely one of the hardest Test matches I have been involved in. That's the type of character we want to build on for the Test in Scotland next week and, looking at the bigger picture, next year's World Cup, when we have Wales in our pool."
And Botha was full of praise for Wales, who with James Hook at centre and Lee Byrne available at full-back looked a far more threatening attacking proposition than they had against Australia seven days previously.
"They played like the Sharks played against the Bulls in the Currie Cup semi-finals, trying to swallow up forwards on the short side before spreading it wide," he continued.
"I truly believe they wanted to shift our big pack around and they did it very well. We showed a lot of character to push ourselves to our limits and fight it out to the 84th minute of the Test.
"But they definitely showed some class against us. We are very pleased to have pulled through."
Saturday's win followed up victory over Ireland in Dublin and puts South Africa within two wins of a first successful Grand Slam tour of the home nations since their 1960-61 trip here.
Scorers: Wales: Tries: North (2), Hook. Cons: S Jones (2). Pens: S Jones (2). South Africa: Tries: Alberts, Matfield. Cons: M Steyn (2). Pens: M Steyn (5).
Wales: Byrne, North, Shanklin, Hook, S Williams; S Jones, Phillips; James, M Rees, A Jones, A Wyn Jones, Davies, Powell, M Williams, Thomas.Replacements: Bennett for Rees (72), Yapp for James (71), R Jones for Powell (60), D Jones for A Wyn Jones (73), R Rees for Phillips (69), Bishop for Shanklin (39-41 mins, bloodbin), Czekaj for S Williams (43)
South Africa: Aplon, Basson, F Steyn, De Villiers, Habana; M Steyn, Pienaar; J du Plessis, B du Plessis, Mtawarira, Matfield, Botha, Spies, Smith, Stegmann. Replacements: Ralepelle for B du Plessis (73), Van der Linde for J du Plessis (75), Van der Merwe for Botha (60), Alberts for Stegmann (46), Hougaard for Pienaar (59), Kirchner for Habana (73), Lambie for M Steyn (67).
Referee: S Walsh (Australia).