Spinner Moeen Ali dismissed Elgar for 46, and pacer Steven Finn got Amla three overs later for 40 to give England a hint of ascendancy at the Wanderers as the tourists chase a first series win over South Africa in more than a decade.
England lead the four-game contest 1-0.
Elgar and Amla were settled, and built a 73-run partnership before Ali created enough turn to find the outside edge of Elgar's bat and have him caught behind by wicketkeeper Jonny Bairstow. Amla also nicked behind, leaving AB de Villiers and Faf du Plessis at the crease.
Ali, Finn and Ben Stokes all had one wicket for England, with Stokes removing Elgar's opening partner Stiaan van Zyl for 21 before lunch.
South Africa, under new captain De Villiers after Amla quit as skipper following the second Test, won the toss and are chasing a way back into the series.
Amla was coming off a double century in the drawn second Test in Cape Town and, relieved of the pressures of captaincy, was in free-flowing form with seven fours. De Villiers began in attacking style, taking one delivery to get his range before hitting Ali for back-to-back boundaries.
England picked an unchanged team from the second test. Offspinner Ali was retained on what's traditionally a fast bowler-friendly pitch.
South Africa went for an all-pace attack, calling up fast bowler Hardus Viljoen for his test debut and dropping spinner Dane Piedt.
Pakistan were now 51 for two.
They had moved on to 76 for two at lunch but Azhar Ali had failed to add to his interval score of seven not out when he was literally knocked off his feet by a Ball yorker and given out lbw by Dharmasena.
But this time, thanks to a tight 'umpire's call' verdict showing the ball clipping leg stump, technology worked in Ball's favour.
Pakistan were now 77 for three but veterans Younis and Misbah, as they had done so often before, steadied the innings.
Their cause was helped when Misbah was dropped on 16 by Joe Root, who grassed a tough slip chance off fast bowler Steven Finn.
Younis struck several elegant drives in his innings but he gave his wicket away on 33 when he clipped Broad straight to Moeen Ali at square leg to end a stand of 57 with Misbah that had had taken Pakistan to 134 for four.
Earlier, as expected, left-arm quick Amir was selected for his first Test appearance since the infamous 'spot-fixing' clash against England at Lord's in 2010.
That match saw Amir and Pakistan new-ball partner Mohammad Asif deliberately bowl no-balls on the instructions of then captain Salman Butt as part of a newspaper 'sting' operation.
All three received five-year bans from cricket and jail terms.
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