Paceman Mohammad Abbas removed opener de Bruyn in the fourth over of today’s play, after Pakistan were bowled out in the last over of the third day for 294 on Saturday, leaving South Africa 41 runs to win.
Dean Elgar (24*) and skipper Faf du Plessis (3*) saw the chase through to win the series.
Half-centuries by Shan Masood, Asad Shafiq and Babar Azam enabled Pakistan to avoid an innings defeat and take the Test into the fourth day. A provision for an extra half hour was not used on Saturday because only 20 minutes or five overs of play would have been possible.
Masood hit a composed 61 and Shafiq and Azam both played aggressively to score 88 and 72, respectively.
Dale Steyn and Kagiso Rabada both took four wickets to get South Africa to the brink of victory.
Steyn drew level with Richard Hadlee of New Zealand in tenth place on 431 wickets on the all-time Test wicket-takers list.