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Pakistan were 176 for six at tea, still 77 runs short of an innings defeat which would complete a 3-0 series sweep for South Africa.
An early finish seemed in prospect when Pakistan lost four wickets quickly after lunch to be floundering at 114 for six, but Sarfraz Ahmed (27 not out) and Saeed Ajmal (30 not out) batted enterprisingly and with a modicum of luck to put on an unbeaten 62 for the seventh wicket.
Azhar Ali and Imran Farhat defied the South African bowlers for most of a morning during which only the wicket of Younis Khan fell.
They saw Pakistan through to lunch at 87 for two, with Azhar on 27, eked out over 110 balls.
But Azhar did not face another ball before he was run out by a superb throw from fine leg by Dale Steyn after being sent back by Farhat, who had initially been seeking a second run.
Pakistan's hopes of avoiding an innings defeat crumbled as three more wickets fell in quick succession.
Farhat was caught behind, slashing at first innings bowling hero Kyle Abbott for 43 and without addition to the score Pakistan captain Misbah-ul-Haq edged an away-swinger from Rory Kleinveldt to wicketkeeper AB de Villiers.
Asad Shafiq made only six before he drove Kleinveldt to mid-off. But Sarfraz and Ajmal showed spirit in batting through until tea.