Stokes was on a hat-trick on the fourth evening of the third Investec Test after making short work of Quinton de Kock and then South Africa captain Faf du Plessis.
The all-rounder was a first-innings centurion for good measure in a match England are strong favourites to win after the tourists reached stumps on 117-4 in pursuit of a notional world-record target of 492.
Joe Root’s men therefore need just six more wickets to go 2-1 up, with one Test to come at Old Trafford.
As well as his wickets, Stokes ruffled stoic opener Dean Elgar with an early bouncer in a particularly hostile spell from the pavilion end – a performance which had frontline seamer Broad likening his team-mate’s abilities to those Andrew Flintoff once served up for England.
“Today, he bowled as quickly as I’ve seen him bowl,” said Broad.
“He had the wind behind him; his tail was up, and I think that bouncer that hit Elgar early in his spell really fired him up.
“From mid-off, it felt very quick – and the slips were pretty impressed.”
Elgar came through the challenge alongside Temba Bavuma, reaching 72 in an unbeaten stand of 65.
Even so, Broad added: “It felt like one of those intimidating spells that Flintoff used to bowl – just heavy, and at the batsman.
“It was great to get two key batsmen out in quick succession with genuine pace.
“It was an exciting session to be on the field. When Stokesy gets that sort of momentum, it’s great to see.
“He certainly dragged the team with him there, and we hope he can have another spell like it tomorrow.”
The key for England is to get the best out of their hugely-talented match-winner as often as possible – and Broad thinks he knows how that is done.
“He’s a better cricketer when he’s in a battle, when he’s fired-up – and the team are learning how to get him in that sort of mode more often.
“He’s such a great competitor to have on your team; if you can stoke him up so he gets in a battle, he has that steely focused look about him. He was pumped-up for that spell this afternoon – there’s no doubt about that ... he got the crowd behind him.”
Stokes was unable to join in as he might have hoped in England’s 313 -8 declared, making 31 while three others passed 50 for the hosts.
In the end, though, Broad senses that comparative disappointment probably helped his bowling.
“He was frustrated at how he got out. It was a good time for him to get the ball and he made a big difference. You want him batting or bowling in key moments.
“I think he’s always a better bowler when he’s using his bouncer and today was no different.”
Elgar stood firm, having already suffered a badly-bruised finger while bowling himself and needing regular attention during his innings.
South Africa assistant coach Adrian Birrell was not surprised by the opener’s characteristic bravery.
“He has a very swollen finger and I have just walked past him with ice in a cup (on it),” he said.
“(Even) if it was broken, that wouldn’t make any difference. He will bat with a broken finger. That won’t be a problem.”
Despite the barrier put up by Elgar and Bavuma, Broad expects to win and head up to Manchester with an unassailable advantage.
Asked if he was confident, he said: “Yes, of course. Obviously, you back yourself to get six wickets on a day-five pitch.”
He has identified signs of variable bounce, but knows England will still have to work hard to achieve their aim.
“I don’t think the pitch has done heaps today to be honest,” he said.
“I think it seamed more on day one and day two, and swung with the overheads.
“As soon as the sun comes out, it’s played a bit better for the batsmen.
“But you’ve always felt in the game with the ball.”