Rickelton made 176 not out as South Africa piled up 316 for four. He shared a fourth-wicket partnership of 235 with his captain, Temba Bavuma, who made 106.
A poor day for Pakistan was made worse when it was announced that opening batsman Saim Ayub had been ruled out of the rest of the game with a right ankle injury.
Ayub fell awkwardly in the outfield in the seventh over of the day. He was taken to the dressing room on a mobile stretcher.
"He is feeling low," said teammate Salman Agha. "He is feeling low but I wish him well and I hope he can come back soon."
While Pakistan gave a lacklustre performance which included only bowling 80 overs in six-and-a-half hours, the left-handed Rickelton enjoyed the best day of his career.
"I played the kind of innings I wanted to play," said Rickelton after striking 21 fours and a six in a 232-ball innings which included some sparkling stroke play.
It was the sort of batting that got him into international cricket – but which he had seldom been able to produce on the big stage.
Even though he made a century against Sri Lanka just two Test matches earlier, Rickelton had struggled to establish himself as a first-choice player since making his Test debut in March 2022.
A hard-fought century against Sri Lanka was a display of grit rather than dazzle after his first 12 Test innings had not produced a single half-century.
"That wicket (in Gqeberha against Sri Lanka) was a bit two-paced with variable bounce. This wicket was level-paced and I always felt I could be in control."
Rickelton, 28, said he had put his early-career struggles behind him after being dropped and left out of a tour of Australia two years ago. "The team has changed, the environment has changed, I just want to bat, I want to score runs."
There was a challenge early on when South Africa lost three wickets for 72 runs before lunch.
"We lost the first session but we knew the wicket was playing well," said Rickelton.
"We knew we needed to maximise our first innings because I think it will take quite a lot of turn later on. Temba emphasised doing the basics and playing straight and we tried to do that."
Bavuma recorded the fourth Test hundred of a career in which he has made 24 half-centuries. He was out 15 minutes before the close, caught behind off occasional off-spinner Agha. He hit nine fours and two sixes in a 179-ball innings.
Agha took two wickets on an otherwise poor day for the Pakistan bowlers. "Things did not go the way we wanted them to go," he said, "but we have to come tomorrow and try to get them out."
