South Africa smashed 343 for nine before Du Plessis declared the innings closed and gave the South African pace attack a four-over spell in which to target the weary England openers.
Keaton Jennings survived the fateful finger of umpire Paul Reiffel when a DRS-referral showed that the ball from Morne Morkel would have cleared his middle stump when on 0 and the decision was overturned.
Alistair Cook and Jennings survived a testing spell as their technique and temperament were scrutinised by both Morkel and Vernon Philander.
Both moved the ball appreciably and launched at least three vociferous appeals. Only height saved the England batsmen.
England limped to 1 without loss at the close on Sunday.
Earlier, Amla underlined his credentials as a world-class batsman with a classy 87. Elgar was composed and aggressive in compiling 80.
"I have a big smile on my face but there is a long road to go," Elgar told Sky Sports.
"Our message after Lord's was that we hadn't become bad players overnight and that we should clear our minds and put those bad thoughts to bed," added Elgar.
"We have a lot of character and we wanted to show it."
Du Plessis’s classy 63 contained several attractive shots and the placement of his offensive strokes were five-star.
Philander hammered an entertaining 42 off 75 balls. It included three fours and two successive sixes, exemplifying his improved ability with the blade.
The defiant and gritty Amla and Elgar added 135 runs in 36.2 overs for the second wicket to put South Africa in charge.
Amla and Du Plessis added another 62 for the fourth wicket to put the Proteas in the ascendancy.
Elgar was dropped on 26 in the gully when James Anderson could not hold onto a very difficult diving chance.
