South Africa were 107 for one at lunch after winning the toss. Test debutant Stephen Cook was 46 not out and Hashim Amla was on 34.
Dean Elgar and Cook put on 35 for the first wicket before Elgar was caught by Taylor off Moeen Ali for 20 when the off-spinner was brought into the attack in the 11th over.
Elgar went for a pull shot and Taylor took avoiding action but the ball lodged between his legs and he was able to grab hold of it before it touched the ground.
In contrast to his father, Jimmy, who was dismissed first ball on his Test debut against India in 1992/93, Stephen Cook scored four off the first ball he faced, a leg side half volley from James Anderson.
Jimmy Cook did, however, make a century on debut against an English team in a 'rebel' international 11 seasons earlier.
Cook looked composed and well-organised in seeing off the new ball in overcast conditions. He had faced 91 balls and hit seven fours at the interval.
Cook was picked ahead of Stiaan van Zyl, batsman JP Duminy replaced Faf du Plessis, while off-spinner Dale Piedt and seamer Kyle Abbott came in for Chris Morris and Hardus Viljoen. Quinton de Kock returned after injury to keep wicket in place of Dane Vilas.
Chris Woakes replaced the injured Steven Finn in the only change in the England team.
England hold a winning 2-0 lead in the series.
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