Despite the hosts’ preparations being overshadowed by the text message saga involving Kevin Pietersen, Finn and James Anderson took three wickets each, although South Africa improved before the close of play.
The Proteas were reduced to 54-4 at one stage but illustrated the depth of their batting line-up to frustrate Andy Flower’s side, as JP Duminy top scored with 61.
“We’re 11 guys who just want to go out and play,” Finn told Sky Sports.
“After Monday everything was swept under the carpet. We’ve got through tough times together in the past and we showed that again today.
“It would have been nice to bowl them out but it is good that we stuck to our guns. No-one got away from us and when the sun is out here it’s a good place to bat.
“Hopefully it will be overcast in the morning and we’ll get the three wickets early.”
Strauss made two changes to the side ahead of the must-win encounter, with Jonny Bairstow and Graeme Swann replacing Pietersen and Tim Bresnan.
It was a record-breaking day for both captains – Strauss became the ninth Englishman to bring up a century of Test-match appearances, while Graeme Smith made it 94 games as skipper, beating the total set by Australian legend Allan Border.
After an even start to the morning’s play, Anderson claimed the first wicket as he forced Smith to edge behind to Matt Prior.
Umpire Kumar Dharmasena initially turned down vociferous appeals from the home players but a review confirmed the batsman’s demise.
South Africa soon managed to settle back into a rhythm after their captain’s departure but a quick-fire trio of scalps from Finn turned the game on its head.
First, Alviro Petersen departed before an inswinging delivery nipped back and caught the off stump of Hashim Amla.
The third of Finn’s dismissals came soon after, with a second successful review showing that the England bowler’s delivery had touched the glove of Jacques Kallis.
It proved to be a controversial decision as replays showed that the glove was off the bat when it made contact.
After lunch, Jacques Rudolph and AB de Villers made life difficult for the hosts as they looked to get the visitors’ innings back on track.
Despite being on top, De Villiers fell shortly after pushing South Africa past 100, with his edge being snapped up by Alastair Cook.
JP Duminy and Rudolph were proving to be tough opponents as they produced stubborn batting displays to bring up a 50 partnership.
But the latter was soon dismissed as Swann’s switch to the Nursery End paid instant dividends.
A short ball looked to be easy pickings for Rudolph but he nicked it onto his stumps after an attempt to work it into the leg side.
Incredibly, this was the Nottinghamshire spinner’s first Test wicket since May’s Trent Bridge meeting with the West Indies.
The arrival of Vernon Philander signalled the beginning of the Proteas tail-end but they continued to frustrate England.
In an attempt to break the stubborn partnership, Strauss took the new ball with just 10 overs left in the day’s play.
The move worked instantly for the captain as Duminy was dismissed – despite being patient for the duration of his knock, he swiped at a wide delivery from Anderson and gave the keeper a fourth catch of the innings.
That would prove to be the last loss of the day for the visitors as Philander (46) and Dale Steyn (21) survived everything that England threw at them.
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