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Centurion: South Africa will need a further seven wickets for a consolation victory on the final day in Centurion after reducing England to 52-3.
The hosts resumed 175 runs ahead on 42-1 and James Anderson captured two early wickets, captain AB de Villiers falling for a second duck in the match.
But ex-skipper Hashim Amla made a solid 96 and Temba Bavuma an unbeaten 78.
The hosts declared on 248-5 to set a nominal target of 382, and the tourists lost both openers inside seven overs.
Anderson's double-wicket burst in the fifth over of the day had briefly raised English hopes of a remarkable win, leaving the South Africans 182 ahead with seven wickets remaining.
But those were emphatically crushed by Amla's determined innings and the terrible start to the England innings as South Africa maintained the their quest to end with only a 2-1 defeat, having lost the series with defeats in Durban and Johannesburg.
Brief scores
South Africa - 475 (de Kock 129*, Cook 115, Amla 109, Stokes 4-86) and 248/5 dec (Amla 96, Bavuma 78*, Anderson 3-47)
England - 342 (Cook 76, Root 76, Ali 61, Rabada 7-122) and 52 for 3 (Rabada 2-15)
Status - England need 330 runs to win
