Jonny Bairstow made a run-a-ball fifty as England left South Africa needing to rewrite the record books if they were to pull off an astounding win in the third Test.
England set South Africa a colossal victory target of 492 in the 100th Test at The Oval when captain Joe Root declared his side's second innings on 313 for eight shortly before tea on the fourth day.
The most any side have made to win in the fourth innings of a Test is the West Indies' 418 for seven against Australia at St John's in 2002/03.
And the largest fourth innings total in a Test at The Oval is the 429 for eight posted by India against England in 1979, when Sunil Gavaskar struck a superb double century in a thrilling draw.
A draw now appeared to the only realistic aim for South Africa in this match, with the tourists needing to bat out a session plus Monday's last day to keep the four-match series all square at 1-1 heading into next week's finale at Old Trafford.
Keshav Maharaj took two wickets for no runs in four balls shortly after lunch to remove the well-set duo of debutant Tom Westley (59) and Root (50).
But Stokes, whose 112 in a first-innings total of 353 helped establish England's strong position in this match, kept the runs coming with a brisk 31.
Bairstow, whose fifty featured six fours, then scored rapidly.
Meanwhile Toby Roland-Jones, once more enjoyed himself with the bat on his Test debut by hitting two sixes in his 23 not out.
England knew that if Middlesex seamer Roland-Jones produced anything like his stunning return of five for 57 — which included all of the Proteas' top four — in the tourists' meagre first-innings 175, they would be well on their way to victory.
Root's men resumed today on 74 for one, already a lead of 252.
Keaton Jennings was 34 not out and Westley 28 not out.
South Africa-born and raised Jennings was under pressure for his place after a run of low scores, including a duck in the first innings of this match.
But in sight of a morale-boosting fifty, the left-handed opener was caught in the gully for 48 off a sharply rising ball from fast bowler Kagiso Rabada.
Westley, meanwhile demonstrated many of the grafting qualities England's critics said they lacked during a massive 340-run defeat in the second Test at Trent Bridge.
The Essex right-hander added just nine runs.
But when Vernon Philander, who had spent Friday night on a hospital drip, pitched short outside off stump, Westley eased him behind point for an elegant boundary.
The seamer did go past Westley's outside edge several times, however, as did Morne Morkel.
But the composed Westley clipped fast bowler Morkel off his pads for a boundary that saw him to a 119-ball fifty, including nine fours.
Shortly after lunch, left-arm spinner Maharaj had Westley stumped before Root holed out in the deep.