Cook finished on 114 not out, his chanceless effort coming after he lost captain and opening partner Andrew Strauss to the fourth ball of the morning before enjoying impressive second-wicket stand of 170 with Jonathan Trott, who made 71.
South Africa fought back late on with the strike of Kevin Pietersen (42) in the last hour after he gloved a short Jacques Kallis ball to wicketkeeper AB de Villiers, who was playing instead of the retired Mark Boucher. Ian Bell was ten not out.
Strauss went lbw to Morne Morkel for a duck, though what could have been a series-defining early strike was cancelled out by Cook and Trott, who eventually edged Morkel to de Villiers. Morkel had figures of two for 44 at stumps.
Left-hander Cook drew level on 20 test hundreds with his mentor and former England captain Graham Gooch, as well as a clutch of distinguished batsmen such as Ken Barrington, Younus Khan, Pietersen, Mark Waugh and Aravinda de Silva.
England, who won the toss when there was rain in the air before the sunshine broke through after lunch, are seeking to hold on to their top ranking in test cricket, as South Africa can leapfrog them if they win the three-match series.
Strauss departed after an initial 'not out' decision by umpire Steve Davis was overturned after a Proteas review, which revealed the ball would have struck the top of middle stump.
Morkel had to wait another 56.4 overs before adding Trott, who played an uncharacteristically loose drive outside off stump. Nevertheless, it was another imposing stand to follow the 329 and 251 that Trott and Cook had shared previously.
Although England started badly, the seemingly indomitable Cook and the equally dependable Trott fought back with a dogged spirit and punished anything wayward.
Cook reached his half-century with a slapped pull shot off leg-spinner Imran Tahir over midwicket for four when the bowler dropped short in his length.
Trott's 50 came up with possibly the best shot of the day, and certainly the most elegant, when he effortlessly pushed a Dale Steyn ball through extra cover for four.
The tone was set early when 13 came off world number one-ranked bowler Steyn's sixth over, including a pulled six by Cook over fine leg. Cook reached his century with a single through cover off Tahir and looked skywards with a sense of achievement.
Pietersen's wicket lifted the gradually wilting tourists and demonstrated that, despite his flamboyant stroke play, he is slightly vulnerable to taking on the short ball.
The pitch was flat and is expected to turn later in the match. The start was delayed by 15 minutes because of a shower.
