Left-arm spinner Noman Ali completed a 10-wicket haul and seamer Shaheen Shah Afridi took the last three wickets as South Africa, who were 51-2 overnight, were dismissed for 183 in the middle session.
The slow and deteriorating wicket proved far too testing for the tourists although Dewald Brevis offered them hope as he bludgeoned a quick-fire half century.
South Africa were always going to be up against it when Tony de Zorzi, who scored a century in the first innings, was trapped leg before wicket by Shaheen Shah Afridi in the first over of the morning, as they chased a target 277 to extend a 10-test winning streak.
It was a rare wicket for a seamer in a contest where neither side used them much, such was the spin-friendly condition of the turning wicket.
Tristan Stubbs lasted only eight balls before a viciously turning delivery from Noman deceived him, bringing Brevis to the wicket.
The 22-year-old already has a reputation in limited overs cricket for his expansive hitting and did not temper his approach in his third test appearance.
He made up for his first ball dismissal in the first innings with 54 runs off as many balls as he put the pressure back onto the Pakistan bowlers and offered South Africa the brief potential of an unlikely win.
Together with Ryan Rickelton they put on a 73-run partnership, but Noman had the last laugh with a turning delivery that clean bowled Brevis.
Rickelton then got a leading edge to Sajid's turning ball to depart for 45, leaving the tourists 137-6 at lunch.
The last four wickets fell without much resistance with Afridi given another spell to wrap up the tail and return figures of 4-33. Noman took 4-79 to add to his six wickets in the first innings.
Defeat for South Africa marked a losing start to the defence of their World Test Championship crown at the beginning of a new two-year cycle.
Next week's second test will be played in Rawalpindi.