At lunch, the tourists were 10 without loss in reply to England's first innings 458 all out which saw Root mark his first innings as England captain with 190.
South Africa captain Dean Elgar was nine not out and Test debutant Heino Kuhn one not out.
England twice lost two wickets for no runs in three balls on Friday after resuming on 357 for five.
Root, missed several times by South Africa, had led a fine recovery after England had collapsed to 76 for four before lunch on Thursday and he resumed on 184 not out, with Moeen Ali unbeaten on 61.
Root's innings was already the highest score by an England captain in his first Test in charge, surpassing Alastair Cook's 173 against Bangladesh in 2010.
But Morne Morkel rocked England with two wickets for no runs in three balls to leave the hosts 367 for seven.
The 26-year-old Yorkshireman walked off to a standing ovation from a capacity and sun-drenched crowd, having batted for over six hours, facing 234 balls including 27 fours and a six.
Root's exit meant the 239 made by New Zealand's Graham Dowling against India at Christchurch in 1968 remained the highest score by a captain in their first Test in charge,
Two balls later Liam Dawson -- selected as much for his lower-order batting as his left-arm spin -- was lbw to a tall fast bowler Morkel for a duck on home debut.
Ali, closing in on a sixth Test century, was bowled between bat and pad for 87 aiming a booming drive off Kagiso Rabada and tailender Mark Wood was lbw for nought.
But Broad, who made his Test-best 169 against Pakistan at Lord's in 2010, kept the runs coming with shots worthy of his father Chris, the former England opener.
He pulled Morkel for two sixes in as many balls to complete a spirited 45-ball fifty also including seven fours.
It was Broad's most fluent Test innings since he was hit in the face by a bouncer from India's Varun Aaron that found a way between the peak of his helmet and the grille at Old Trafford in 2014.
He was last man out when caught behind off Morkel, who led the Proteas' attack with four for 115 in 25.3 overs.
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