Du Plessis fell for 98 but De Kock was 75 not out as South Africa reached 278-5 in reply to Zimbabwe's first-innings total of 256 at Harare Sports Club. Their partnership for the fifth wicket was worth 119.
Du Plessis hit 11 fours and was on the brink of a fourth test century when he fell just before lunch to give offspinner John Nyumbu one of his three wickets on his debut.
The two batsmen nearly took South Africa through the first session unscathed but Du Plessis advanced down the pitch three overs before the lunch break and clipped a catch to backward square leg to fall two short of a hundred.
Nyumbu, one of two Zimbabweans making their test debuts in the first five-day match between the neighbors in a year, had 3-105 to lead the home bowlers. Donald Tiripano, Zimbabwe's other debutant, and Tendai Chatara had one wicket each.
The South Africans' progress was slow as they scored at less than 2 ½ runs per over and De Kock also changed his normally attacking game to hit just five boundaries.
Opener Dean Elgar made 61 on Sunday at the start of South Africa's reply, but the dangerous AB de Villiers and Hashim Amla both failed to reach double figures and the South Africans fought hard for their lead.
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