With Joe Root on 106 not out overnight, England appeared on course for a significant first-innings advantage on the third day which could have taken the series out of South Africa's reach.
But Kagiso Rabada sent Root back for 110 early in the first session, and South Africa took regular wickets to stay in the game. Rabada had career-best figures of 5-78.
South Africa had wiped out England's lead by lunch as the home team reached 16-0 in its second innings, a lead of six to leave the match evenly balanced.
England leads the four-test series 1-0 over the top-ranked South Africans.
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