Hashim Amla's innings of 121 had taken South Africa to 351 all out, leaving them a fourth-innings target larger than they have ever previously managed.
And they made the worst possible start, losing Alastair Cook for just three, and then Strauss for one as Vernon Philander struck twice late in the day.
Jonathan Trott and Ian Bell survived to stumps, but England now require 330 runs in 90 overs on a day five pitch to secure a 1-1 draw in the series and with it retain their status as the world's best Test side.
The day had begun with the Test in the balance, but resistance from Dale Steyn, who faced a barrage of short balls before being dismissed for nine, helped Amla settle in at the crease.
The triple-centurion from The Oval then formed a solid partnership with AB de Villiers (43) worth 95 runs - though the Proteas' wicketkeeper had an awful drop from James Anderson at midwicket for keeping him at the crease in the morning session.
Despite a forecast of clear skies and fine weather, a storm interrupted play for 20 minutes on either side of lunch. It did not affect the rhythm of the batting duo, who negotiated the first few overs of the second new ball with ease.
The game was slipping away until an inspired burst from Steven Finn threatened to wrest the initiative back.
He bowled Amla with a peach of a ball - and a near-copy of the delivery which accounted for him in the first innings - before drawing edges from de Villiers and then Jacques Rudolph (11).
England needed to wrap the innings up quickly before the total grew any more imposing, but a nagging partnership from JP Duminy and Philander put paid to thank. Philander's brisk 35 stretched the home side's patience, though his exit was timid, after he steered a wide ball from Anderson to point.
Some quick thinking from Matt Prior to stump Morne Morkel accounted for Graeme Swann's only wicket of the day - he was economical but largely unthreatening - before Anderson clean-bowled Imran Tahir.
It freed the South African bowlers up for a 13-over examination of England before stumps - an examination they failed.
Cook ended a low-key series being rapped on the pads for a leg-before decision that was not worth wasting a review on.
Strauss's was worse - on his 100th Test, his decision to leave a straight ball that was bound for the stumps looked like the product of a frazzled mind.
Ordinarily that would have brought Kevin Pietersen to the crease - but the fate of Strauss' side now rests in the hands of his young charges, and the task could scarcely be harder.