Broad excelled once again in the absence of James Anderson, clean bowling opener Stiaan van Zyl and taking out key duo Hashim Amla and AB De Villiers with some formidable seam bowling.
The Proteas bowled the tourists out in the morning for 303, and finished the day 137-4, a deficit of 166.
But it was also a day of missed opportunities for the tourists, who twice failed to review not out decisions that would have been overturned and saw a seemingly clean catch from Ben Stokes chalked off by third umpire Bruce Oxenford.
De Villiers was on 11 at that time and went on to make 49, while Dean Elgar finished on 67no having survived a Stokes lbw appeal that would have been given had Alastair Cook called for DRS.
But griping about technology and its use must be secondary to Broad’s brilliance.
When he is in full flow, hitting a slightly fuller length and threatening off stump, there are few finer sights for an England cricket fan.
When Anderson missed the fourth Ashes Test last summer, Broad turned in career-best figures of 8-15 to blow Australia away, and although this was less spectacular, he bowled with great control and admirable intelligence.
His second ball had Stiaan van Zyl caught in the headlights, the out-of-form opener withdrawing the bat and watching as off stump was flattened.
Four balls later Broad went up for a caught behind against home captain Amla, but Cook did not seem fully convinced and declined to review Aleem Dar’s not out decision.
Although there is no infra-red technology in the series, replays seemed to suggest a tiny edge.
Amla is not a man to let off early, something England fans will know after his triple century at the Oval three years ago, but he was offered another life moments later.
This time Chris Woakes drew the nick only for wicketkeeper Jonny Bairstow to put down the catch, diving one-handed to his right.
It all felt terribly ominous until Amla ran out of luck at the third attempt, Broad producing a beauty that was asking to be nicked on the back foot.
De Villiers might also have gone cheaply, Finn locating the edge and Stokes gathering low at gully, but a familiar sequence of events soon began to unfold.
Dar referred the decision to Oxenford, whose slow motion replays served only to cloud the issue and create doubt before the batsman was reprieved.
De Villiers set about cashing in either side of tea, putting on 86 with Elgar.
But Broad refused to let the game slide, unsettling De Villiers with a frustrating line outside off stump then drawing the error with a perfectly-pitched leg-cutter.
Broad sprinted away in celebration, fully aware how important that breakthrough could be.
Elgar brought up the first half-century of the innings with a pick-up six off Moeen Ali, who shipped 40 from his first eight overs.
But the game had another curious twist up its sleeve.
Faf du Plessis danced down the pitch and looked a certainty to be stumped.
Instead, the ball brushed the off bail so gently there was a moment of confusion before the batsman’s fate was confirmed.
It should have been 117-5 soon after but, incredibly, another wicket went begging due to an unused review.
This time Stokes rapped Elgar, on 58, on the knee-roll and went up for lbw.
He failed to convince either Dar or Cook, whose reticence to review again proved costly.
English hopes of posting at least 400 had earlier evaporated in an three-hour morning session that saw them stumble from their overnight 179-4.
Morne Morkel and Dale Steyn each finished with four wickets, the former dismissing Stokes, Nick Compton, Moeen and Woakes to claim the pre-lunch momentum. Compton, 63no overnight, had batted with trademark grit in pursuit of a century in the city of his birth, eking out seven runs in the first hour.
But he had to settle for 85, feathering a Morkel bumper behind after almost six-and-a-half hours in the middle.
Morkel then made it three wickets in six deliveries, dismissing Moeen and Woakes for back-to-back ducks. Broad knows a thing or two about those, having taken two and been a victim of Peter Siddle’s five years ago, but Morkel narrowly missed his outside edge with the hat-trick ball.
Kyle Abbott ended Bairstow’s stay for 41 before England nudged past the 300-mark courtesy of a 36-run last-wicket stand between Broad and Finn.