Pakistan opening bowlers Mohammad Abbas and Khurram Shahzad struck three blows late on the third afternoon as South Africa set out in pursuit of 148 runs to win the first Test at SuperSport Park on Saturday.
South Africa were reeling at 27 for three at the close, 121 runs short of a victory which would clinch them a place in the World Test championship final in England next June.
Abbas took two wickets for three runs in four immaculate overs of swing bowling, dismissing Tony de Zorzi and Tristan Stubbs, while Shahzad trapped Ryan Rickelton.
Aiden Markram, South Africa's top scorer in the first innings, was unbeaten on 22 going into what could be a nervy fourth day for the hosts.
All three wickets were leg before wicket decisions – and all three were reviewed.
De Zorzi batted outside his crease in an attempt to counter the swing which undid him in the first innings – but Abbas beat his inside edge and he was given out.
He reviewed umpire Alex Wharf's decision but replays showed the impact was "umpire’s call", with the ball going on to hit the stumps, and he had to go for two runs.
Rickelton failed to score before he was trapped by Shahzad and Stubbs made one before falling to Abbas – with Pakistan successfully reviewing on both occasions after the batsmen were initially given not out.
It was a dramatic end to a day on which the start was delayed by three hours because of rain.
South Africa seemed well on target for victory when Pakistan were bowled out for 237, with left-arm fast bowler Marco Jansen taking six for 52.
Saud Shakeel made 84 for Pakistan.
Resuming at 88 for three, Babar Azam and the left-handed Shakeel batted confidently, adding another 65 runs in 14.5 overs.
Babar made 50, his first half-century in 19 Test innings, before Jansen had a burst of three wickets in 14 balls, starting when Babar slapped a short ball from Jansen to deep point.
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Shakeel was ninth man out when he missed a full toss from Jansen after hitting 10 fours and a six in a 113-ball innings.