He grew in confidence and along with Hashim Amla, who also scored a wonderful century, shared a 202-run stand.
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The opener Stiaan van Zyl was going through bad form so he was finally dropped and Cook, who was having a great domestic season was brought in.
The Proteas had resumed after tea on 224/1, but finished the day 329/5.
South Africa suffered a blow in the 11th over when Dean Elgar (20) was caught out by James Taylor off Ali’s delivery, but the hosts did not wobble as Hashim Amla and Cook guided the attack.
Alastair Cook, the England skipper, said he hoped his side would continue to be as “ruthless” as they were in Johannesburg. They played well, we missed our lengths. It was a massive challenge and we have done it. It’s really rewarding. “That last session is our benchmark for tomorrow morning”.
The England vice-captain, Joe Root jumped to the defence of the England bowlers after the first day of their dead-rubber fourth Test with South Africa, insisting their early struggles with the ball were down to human error.
Amla survived an early scare as he was dropped by Alastair Cook at first slip after edging Ben Stokes while in single figures.
That had included a wicketless afternoon session that had seen Anderson warned again for running on the pitch.
This on a first day full of incident in the fourth Test against England at SuperSport Park in Centurion on Friday.
It was just another setback for the 33-year-old on a luckless day.
South Africa are without a batting coach and that is one of the issues De Villiers is eager to address.
The tourists already have an unassailable 2-0 lead in the series, but with home series against Sri Lanka and Pakistan and trips to Bangladesh and India still to come this year, there are positions to be firmed up, especially at the top of the order.
South Africa’s next Test series comes against New Zealand in August.
England replaced injured fast bowler Steven Finn with Chris Woakes as it chases an eye-catching 3-0 series victory in South Africa.
But Cook, whose father Jimmy was dismissed first ball on his debut for South Africa in 1992 at the age of 39, looked organised from the start, hitting a four off the first ball of the match when James Anderson’s delivery strayed down leg side.
Dane Vilas, who substituted in last week’s third Test defeat in Johannesburg, was released to play for his provincial team after De Kock passed a fitness test.
Cook went to his century off 187 balls when he tucked Stokes through midwicket for two and added 15 more runs before edging a ball from Chris Woakes into his stumps.
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Temba Bavuma then came to the crease, but Duminy was out LBW for 16 shortly after when he tried to pull a Moeen Ali delivery that wasn’t quite short enough.
