England need to take six South Africa wickets on the final day of the first Test in Durban to open up a lead in the series.
The tourists reduced the Proteas to 136-4 at the close of play today, meaning that South Africa need 280 more runs if they are to snatch victory.
England started day four 172-3 in their second innings, but Joe Root (73) soon fell before Ben Stokes (5) and James Taylor (42) quickly followed to give South Africa hope of restricting the tourists.
However, Jonny Bairstow's innings-high knock of 79, with partnerships of 48 and 43 with Moeen Ali (16) and Chris Woakes (23) respectively, pushed England to 326 all out with a lead of 415.
In reply, Dean Elgar and Stiaan van Zyl put on an opening partnership of 53 before Van Zyl was bowled by Stokes for 33.
Hashim Amla (12) was next to the crease and he started solidly before edging Steven Finn through to wicket-keeper Bairstow.
Elgar (33) was Finn's next victim and the England paceman then made a crucial late breakthrough in the final over of the day, removing Faf du Plessis for nine.
AB de Villiers is unbeaten on 37 and has been joined by nightwatchman Dale Steyn (0*), who is batting with a shoulder injury.