The wicketkeeper-batsman roared with emotion when reaching three figures, four years after making his Test debut, and was unbeaten on 150 when England skipper Alastair Cook declared on 629 for six.
Afterwards he revealed what his first century in the longest format meant to him and his family.
The Yorkshireman, whose previous highest score was 95 against the Proteas at Lord’s in 2012, told ecb.co.uk: “It meant a huge amount. I think this is my 21st, 22nd Test match and to have played quite a few now and got close, it was really special in many ways.
“It was a lot of things built up, obviously there has been speculation over a period of time about can you do this, can you do that.
“To show people in that fashion that you can do it, people who don’t necessarily come to the county games all the time and only watch international cricket, to say this is how I play my cricket and ply my trade is fantastic.
“The emotion I showed there was not only for my colleagues in the dressing room for having faith in myself but also for my family as well.
“It is obviously a special occasion for us, as a family, my mum and sister and a lot of family friends are here, and there are people who are not here as well. It is for them.
“I was trying to find them because there was a lot of people up there. It is mum’s birthday in a couple of days so it is a nice one for her. It is for everyone who has helped me through what has been quite a journey through my career.”
Bairstow was the perfect foil for double-centurion Ben Stokes during a world-record sixth-wicket stand of 399.
He played the supporting role before cutting loose after making his hundred, hitting 18 fours and a brace of maximums during his 191-ball innings.
On Stokes, he told Sky Sports: “When he’s going like that, like a steam train, I don’t think there’s a need to do anything else.
— Joe Root (@root66) January 3, 2016
“It was unbelievable at the other end to be out there. Some of the strokes that he played were second to none. It was a pleasure to be out there and to put on a stand that we did.
“It was a very, very special day. It is something that I don’t think I’ll ever forget.”
Bairstow is confident England can take 20 wickets to move 2-0 ahead in the series on a Newlands pitch that is still ideal for batting.
“It is going to be a challenge, South Africa are obviously a quality side, so hopefully we can come back in the morning with a bit of reverse swing and conventional swing, if the clouds come in, and then use whatever skills we have created,” he said.
“Our bowling attack is very experienced, they are all going to come back very fresh and raring to go. I have no doubt that we will be able to take 20 wickets.”