Root decided not to enforce the follow despite England leading by 217 runs on the first innings.
South Africa, 2-1 down in the series, would still have held out hopes of a fightback when they had England 318-9 but after leaking runs and then being tumbled out by the touring bowlers, they again have their backs to the wall.
England established complete dominance over a worn and wearied South Africa in Johannesburg, leaving themselves two days to convert their 465-run lead in the fourth Test into a memorable series win.
That would seal a 3-1 success following the celebrations in Cape Town and Port Elizabeth and, with six full sessions to go on a ground where the record chase stands at 310, any other result seems inconceivable.
Fast bowler Anrich Nortje cherished a maiden five-wicket haul in Test cricket.
South Africa were in danger of folding embarrassingly, only for Quinton De Kock and Dwaine Pretorius to add some long-awaited steel with a partnership of 79. He will retire from global cricket next week in favour of a Kolpak contract with Somerset in English county cricket later this year.
De Kock turned his existing 32 into a fourth half-century of the series and Pretorius took advantage of some attacking fields to drive his way to a new personal best of 37.
De Kock did not last long soon after, with Mark Wood going past his defences to remove him for a well-played 76.
A rain-affected Friday had the hosts conceding England's first century partnership for the first wicket since 2016, when openers Keaton Jennings and Alastair Cook starred against India in Chennai.
Joe Denly was played onto his own stumps off Paterson, while Sibley was caught by Malan to become Hendricks' first victim of the day. The incident occurred in the 85th over of England's innings on Saturday, when Philander used inappropriate language after dismissing Jos Buttler, which could have provoked an aggressive response from the batsman.
England succumbed for 248 in 61.3 overs - Joe Root (58) the final wicket to fall to a spectacular catch by Faf du Plessis at gully - with Beuran Hendricks (5-64) taking five-for on debut.
Sam Curran cracked 35 from 29 balls before falling to Hendricks, hooking out to the man in the deep, while the left-armer then snared Woakes for a duck two balls later.