Centuries for Smith, who made 131 in his 100th Test, and Hashim Amla took the Proteas to 403 for two and a lead of 18 at the Oval.
Amla ended the third day 183 not out and will resume today in an unbroken partnership of 143 with Jacques Kallis (82no) as the tourists look to drive home their advantage.
And Smith told Sky Sports News: "It was an outstanding day, we knew we had to make a few plays and we've done that. Now there are two big days left in the Test match."
South Africa have fought back well after Alastair Cook's hundred helped England take the upper hand on day one and Smith continued: "We're a mature unit and we know when we need to step it up.
"It wasn't a terrible day one but there weren't many highlights for us. At 260 for three it would be easy to let the game slide and give England dominance."
England bowling coach David Saker watched his charges struggle for virtually the whole day but said: "They're quite upbeat considering what's happened today.
"The bowlers toiled really well, I couldn't have asked much more of them, and the fielders worked hard but the day belonged to South Africa."
England's bowlers had no answer as Smith and Amla batted through almost three sessions together to set a new highest second-wicket stand for South Africa against England.
Initially, they were sustaining the tourists' recovery. But by stumps, South Africa's 403 for two gave them massive power to add and put England under extreme pressure for the remainder of this first Test.
Smith and Amla reprised what they had witnessed themselves from Alastair Cook and Jonathan Trott two days ago.
England's stone-wallers added a mere 170 in 58 overs after the loss of captain Andrew Strauss for a duck at the very start of this series.
But in reply to 385 and after opener Alviro Petersen had also made nought on Friday, South Africa's captain and No 3 put on 259 together against a home attack rendered toothless on a slow pitch and able to take only Smith's wicket all day.
It is hard to see how England could do anything better than end up trying to save the match, over the last two days. For the first time on home soil since Trent Bridge last year, Strauss' team will trail significantly after the first innings.
Back then, Ian Bell's big hundred put them back in charge on the way to a landslide win over India. There is little time for that sort of outcome here, where the hosts will surely be grateful to grind out a draw to stay in position to defend their table-topping status in this short series.
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