The win was Australia's first on South African soil since 2000 and only their second since 1992, while defeat for the Boks was their third in succession and fourth out of five this season.
The victory sets up a series decider with New Zealand next month, and Kiwi tactician Deans admitted he was delighted to see his players dig deep against a South African side with much to prove after a dismal run of form.
"I'm very happy with our performance, although it was not error free," said Deans, whose side ran in three tries through Benn Robinson, Lote Tuqiri and Stirling Mortlock.
"If you look at the intensity of the game, we did what had to be done but we did it the hard way. Today I am pleased.
"If we look at the momentum of the game, the result was just but it was not straightforward. I am very happy with the composure of the team."
Deans refused to be too hard on his players after they gave away two tries to a Springbok team who had not made it over the line since their 30-28 win over the All Blacks in Dunedin on July 12.
"We let them in towards the end somewhat softly but in any event we were up against a side which is capable," he said. "Most importantly we were patient in the way we met their physicality."
Mortlock was one of the stars of the show, scoring a stunning virtuoso try to seal the win late on, and the Australia skipper admitted to his relief at seeing his team shake off their South African hoodoo.
"I've been here many times and we have fallen short and I am very impressed with this group's performance, especially because it is some of the guys' first times in South Africa," he said.
"Today, all 20 guys showed spirit and determination and played their hearts out."
Springbok coach Peter de Villiers admitted the defeat was unacceptable and said fans were within their rights to boo the team after the game.
The loss ended the world champions' hopes of winning the Tri-Nations, and De Villiers admitted to having an uncomfortable time of it as he and captain Victor Matfield conducted post-match interviews on the pitch.
"It was not nice being out there, especially after I felt we had the firepower to win the game and the opportunities," De Villiers said.
"If we maybe took some of our chances in the first half we would not have found ourselves in this situation.
"The fans have the right to be unhappy. South Africa are a proud nation. They want to be winners and want to back a winning side. We will never go out and lose a game on purpose.
"We have a new playing style that we are trying put out there and Rome wasn't built in a day. We ask that they be more patient on the time they give us to come to grips with what we want to do."