Keshav Maharaj, captaining the Proteas in a Test match for the first time, chose to keep Zimbabwe in the field until his team were bowled out for 369 in their second innings more than half an hour after tea.
All-rounder Wiaan Mulder, in his third match since being promoted to bat at No 3, made his second Test century, batting fluently to score a Test-best 147 before being caught on the deep midwicket boundary off part-time spin bowler Wessly Madhevere.
Zimbabwe were hampered by the absence through illness of fast bowler Blessing Muzarabani. He was off the field for most of the morning which meant he could not bowl until half an hour before tea.
Tanaka Chivanga was the only pace bowler available to captain Craig Ervine for most of the innings, leaving the bulk of the bowling to be done by the spinners.
As in the first innings, South Africa scored at more than four runs an over but left-arm spinner Wellington Masakadza picked up four wickets for 98 runs.
Leg-spinner Vincent Masekesa, who took heavy punishment from debutants Lhuan-dre Pretorius and Dewald Brevis in the first innings, dismissed both youngsters cheaply second time around.
The left-handed Pretorius, who made 153 in the first innings, was bowled for four by a ball which spun back sharply. Brevis added only three to his first-innings 51 before being bowled by a flighted delivery when he went for a big shot.
When the Proteas innings ended there were a minimum of 18 overs to be bowled.
Because of the number of overs bowled by the Zimbabwe spinners, who kept their team ahead of the required over rate, there was a rarity in modern Test cricket in that South Africa were able to squeeze in an extra over before the close – with unfortunate consequences for Zimbabwe.